<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01127698</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-13T10:00:57+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A simple soluble model of discrete sequential fragmentation</title>
            <author role="aut">
              <persName>
                <forename type="first">Renaud</forename>
                <surname>Delannay</surname>
              </persName>
              <email type="md5">e47d8dd40405ee8f50f45fd23b86d0ff</email>
              <email type="domain">univ-rennes1.fr</email>
              <idno type="idhal" notation="string">renaud-delannay</idno>
              <idno type="idhal" notation="numeric">1142</idno>
              <idno type="halauthorid" notation="string">269-1142</idno>
              <idno type="IDREF">https://www.idref.fr/061589659</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8361-9604</idno>
              <affiliation ref="#struct-441232"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gérard</forename>
                <surname>Le Caër</surname>
              </persName>
              <email type="md5">96d214e958717079f1912b2a09dea2eb</email>
              <email type="domain">univ-rennes1.fr</email>
              <idno type="idhal" notation="string">gerard-le-caer</idno>
              <idno type="idhal" notation="numeric">527</idno>
              <idno type="halauthorid" notation="string">14314-527</idno>
              <idno type="IDREF">https://www.idref.fr/052452220</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-5316-7996</idno>
              <affiliation ref="#struct-1127"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">R</forename>
                <surname>Botet</surname>
              </persName>
              <idno type="halauthorid">895645-0</idno>
              <affiliation ref="#struct-134"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Renaud</forename>
                <surname>Delannay</surname>
              </persName>
              <email type="md5">e47d8dd40405ee8f50f45fd23b86d0ff</email>
              <email type="domain">univ-rennes1.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2015-03-07 18:07:41</date>
              <date type="whenModified">2025-11-05 16:08:07</date>
              <date type="whenReleased">2015-03-07 18:07:41</date>
              <date type="whenProduced">1996-11</date>
              <ref type="externalLink" target="https://api.istex.fr/document/B6FA99CA29B30ADC233C22249A2CE04031F72E28/fulltext/pdf?sid=hal"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="195340">
                <persName>
                  <forename>Renaud</forename>
                  <surname>Delannay</surname>
                </persName>
                <email type="md5">e47d8dd40405ee8f50f45fd23b86d0ff</email>
                <email type="domain">univ-rennes1.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01127698</idno>
            <idno type="halUri">https://hal.science/hal-01127698</idno>
            <idno type="halBibtex">delannay:hal-01127698</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Physics A: Mathematical and General (1975 - 2006)&lt;/i&gt;, 1996, 29 (21), pp.6693-6699. &lt;a target="_blank" href="https://dx.doi.org/10.1088/0305-4470/29/21/005"&gt;&amp;#x27E8;10.1088/0305-4470/29/21/005&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Physics A: Mathematical and General (1975 - 2006), 1996, 29 (21), pp.6693-6699. &amp;#x27E8;10.1088/0305-4470/29/21/005&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
            <idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="IJL-UL">Institut Jean Lamour</idno>
            <idno type="stamp" n="LEMTA-UL">LEMTA - Laboratoire d'Energétique et de Mécanique Théorique et Appliquée</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-PSUD-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris Sud pour Paris Saclay</idno>
            <idno type="stamp" n="GS-PHYSIQUE">Graduate School Physique</idno>
            <idno type="stamp" n="LPSO">Laboratoire de Physique des Solides d'Orsay</idno>
            <idno type="stamp" n="URP-LPS">Laboratoire de Psychologie Sociale : contextes et régulation</idno>
            <idno type="stamp" n="EMPP-UL">Pôle scientifique Energie, Mécanique, Procédés, Produits de l'Université de Lorraine</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A simple soluble model of discrete sequential fragmentation</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Renaud</forename>
                    <surname>Delannay</surname>
                  </persName>
                  <email type="md5">e47d8dd40405ee8f50f45fd23b86d0ff</email>
                  <email type="domain">univ-rennes1.fr</email>
                  <idno type="idhal" notation="string">renaud-delannay</idno>
                  <idno type="idhal" notation="numeric">1142</idno>
                  <idno type="halauthorid" notation="string">269-1142</idno>
                  <idno type="IDREF">https://www.idref.fr/061589659</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8361-9604</idno>
                  <affiliation ref="#struct-441232"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gérard</forename>
                    <surname>Le Caër</surname>
                  </persName>
                  <email type="md5">96d214e958717079f1912b2a09dea2eb</email>
                  <email type="domain">univ-rennes1.fr</email>
                  <idno type="idhal" notation="string">gerard-le-caer</idno>
                  <idno type="idhal" notation="numeric">527</idno>
                  <idno type="halauthorid" notation="string">14314-527</idno>
                  <idno type="IDREF">https://www.idref.fr/052452220</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-5316-7996</idno>
                  <affiliation ref="#struct-1127"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">R</forename>
                    <surname>Botet</surname>
                  </persName>
                  <idno type="halauthorid">895645-0</idno>
                  <affiliation ref="#struct-134"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="OLD">27162</idno>
                <idno type="issn">0305-4470</idno>
                <title level="j">Journal of Physics A: Mathematical and General (1975 - 2006)</title>
                <imprint>
                  <publisher>IOP Publishing</publisher>
                  <biblScope unit="volume">29</biblScope>
                  <biblScope unit="issue">21</biblScope>
                  <biblScope unit="pp">6693-6699</biblScope>
                  <date type="datePub">1996-11</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1088/0305-4470/29/21/005</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="phys.cond.cm-gen">Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>A simple model of discrete sequential fragmentation consists in first breaking a unit segment into q(greater than or equal to 2) pieces of equal length. A fragment is then selected at random among all fragments and broken in turn into q pieces of equal length and so on ad infinitum. Fragments of size L = q(-s)(s = 0,..., f) are thus produced after f fragmentation events. The distribution of the ensemble averaged number of fragments of 'size' s is calculated exactly in terms of signless Stirling numbers of the first kind and shown to tend asymptotically to a Poisson distribution with parameter (q/(q - 1))log(f). An asymptotic lognormal distribution is thus found for the distribution of L.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-441232" status="OLD">
          <idno type="IdRef">052488454</idno>
          <idno type="ISNI">0000000121795509</idno>
          <idno type="RNSR">197612609P</idno>
          <idno type="IdUnivLorraine">[UL]RQF--</idno>
          <idno type="ROR">https://ror.org/01pfter31</idno>
          <orgName>Laboratoire d'Energétique et Mécanique Théorique et Appliquée</orgName>
          <orgName type="acronym">LEMTA</orgName>
          <date type="start">1980-01-01</date>
          <date type="end">2023-12-31</date>
          <desc>
            <address>
              <addrLine>Université de Lorraine - ENSEM - ESSTIN, 2 avenue de la Forêt de Haye, TSA 60604, 54518 Vandoeuvre-les-Nancy Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://lemta.univ-lorraine.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413289" type="direct"/>
            <relation name="UMR7563 / URA875" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1127" status="OLD">
          <orgName>Laboratoire de Science et Génie des Matériaux et de Métallurgie</orgName>
          <orgName type="acronym">LSG2M</orgName>
          <date type="start">1971-01-01</date>
          <date type="end">2008-12-31</date>
          <desc>
            <address>
              <addrLine>Ecole des Mines de Nancy Parc de Saurupt 54042 NANCY CEDEX</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-300291" type="direct"/>
            <relation active="#struct-300293" type="direct"/>
            <relation name="UMR7584 / URA159" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-134" status="OLD">
          <orgName>Laboratoire de Physique des Solides</orgName>
          <orgName type="acronym">LPS</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bat. 510 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lps.u-psud.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
            <relation name="UMR8502" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-413289" status="VALID">
          <idno type="IdRef">157040569</idno>
          <idno type="IdUnivLorraine">[UL]100--</idno>
          <idno type="ROR">https://ror.org/04vfs2w97</idno>
          <orgName>Université de Lorraine</orgName>
          <orgName type="acronym">UL</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lorraine.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300291" status="OLD">
          <orgName>Université Henri Poincaré - Nancy 1</orgName>
          <orgName type="acronym">UHP</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300293" status="OLD">
          <orgName>Institut National Polytechnique de Lorraine</orgName>
          <orgName type="acronym">INPL</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-92966" status="OLD">
          <idno type="ROR">https://ror.org/028rypz17</idno>
          <orgName>Université Paris-Sud - Paris 11</orgName>
          <orgName type="acronym">UP11</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-psud.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>