Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "5560"
  #_source: array:26 [
    "id" => "5560"
    "slug" => "chord-distribution-functions-and-rice-formulae-application-to-random-media"
    "yearMonth" => "2007-07"
    "year" => "2007"
    "title" => "Chord-distribution Functions and Rice Formulae. Application to Random Media."
    "description" => "KRATZ, M., ESTRADE, A. et IRIBARREN, I. (2007). Chord-distribution Functions and Rice Formulae. Application to Random Media."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "ESTRADE A."
      ]
      2 => array:1 [
        "name" => "IRIBARREN I."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:1 [
      0 => "Chords"
    ]
    "updatedAt" => "2021-04-19 17:57:25"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => null
      "volume" => null
      "number" => null
    ]
    "type" => array:2 [
      "fr" => "Communications dans une conférence"
      "en" => "Presentations at an Academic or Professional conference"
    ]
    "support_type" => array:2 [
      "fr" => null
      "en" => null
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "We consider a two-phases model to describe a porous medium, an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase. Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato)."
      "en" => "We consider a two-phases model to describe a porous medium, an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase. Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato)."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-26T19:21:52.000Z"
    "docTitle" => "Chord-distribution Functions and Rice Formulae. Application to Random Media."
    "docSurtitle" => "Presentations at an Academic or Professional conference"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, ESTRADE A., IRIBARREN I."
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, ESTRADE A., IRIBARREN I.</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2007</span>"
    "keywordList" => "<a href="#">Chords</a>"
    "docPreview" => "<b>Chord-distribution Functions and Rice Formulae. Application to Random Media.</b><br><span>2007-07 | Presentations at an Academic or Professional conference </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Chord-distribution Functions and Rice Formulae. Application to Random Media.</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 8.957939
  +"parent": null
}