Bifractality of the devil’s staircase appearing in the burgers equation with brownian initial velocity View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1997-09

AUTHORS

E. Aurell, U. Frisch, A. Noullez, M. Blank

ABSTRACT

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil’s staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations. More... »

PAGES

1151-1164

References to SciGraph publications

  • 1992-09. The inviscid Burgers equation with initial data of Brownian type in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1992-09. Statistics of shocks in solutions of inviscid Burgers equation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02732429

    DOI

    http://dx.doi.org/10.1007/bf02732429

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1042874238


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0915", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Interdisciplinary Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Stockholm University", 
              "id": "https://www.grid.ac/institutes/grid.10548.38", 
              "name": [
                "Center for Parallel Computers, Royal Institute of Technology, S-100 44, Stockholm, Sweden", 
                "Mathematics Department, Stockholm University, S-106 91, Stockholm, Sweden"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Aurell", 
            "givenName": "E.", 
            "id": "sg:person.01104576776.49", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01104576776.49"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "name": [
                "Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304, Nice Cedex 4, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Frisch", 
            "givenName": "U.", 
            "id": "sg:person.011615073661.47", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011615073661.47"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "name": [
                "Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304, Nice Cedex 4, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Noullez", 
            "givenName": "A.", 
            "id": "sg:person.01262773202.94", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01262773202.94"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institute for Information Transmission Problems", 
              "id": "https://www.grid.ac/institutes/grid.435025.5", 
              "name": [
                "Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304, Nice Cedex 4, France", 
                "Institute for Information Transmission Problems, 101477, Moscow, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Blank", 
            "givenName": "M.", 
            "id": "sg:person.016626051205.94", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016626051205.94"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02096550", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001608199", 
              "https://doi.org/10.1007/bf02096550"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096550", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001608199", 
              "https://doi.org/10.1007/bf02096550"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096551", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050362339", 
              "https://doi.org/10.1007/bf02096551"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096551", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050362339", 
              "https://doi.org/10.1007/bf02096551"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.39.268", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060478819"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.39.268", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060478819"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1997-09", 
        "datePublishedReg": "1997-09-01", 
        "description": "It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil\u2019s staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf02732429", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1040979", 
            "issn": [
              "0022-4715", 
              "1572-9613"
            ], 
            "name": "Journal of Statistical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "5-6", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "88"
          }
        ], 
        "name": "Bifractality of the devil\u2019s staircase appearing in the burgers equation with brownian initial velocity", 
        "pagination": "1151-1164", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "cc3a34aa6423a9fa50c2e2f3abfe38ad09b08ffbef501157daf665998441c8cd"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf02732429"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1042874238"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf02732429", 
          "https://app.dimensions.ai/details/publication/pub.1042874238"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T17:30", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8672_00000507.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2FBF02732429"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02732429'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02732429'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02732429'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02732429'


     

    This table displays all metadata directly associated to this object as RDF triples.

    102 TRIPLES      21 PREDICATES      30 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf02732429 schema:about anzsrc-for:09
    2 anzsrc-for:0915
    3 schema:author N5fa95482d9b449eaad0e56330958b367
    4 schema:citation sg:pub.10.1007/bf02096550
    5 sg:pub.10.1007/bf02096551
    6 https://doi.org/10.1103/physreva.39.268
    7 schema:datePublished 1997-09
    8 schema:datePublishedReg 1997-09-01
    9 schema:description It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil’s staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.
    10 schema:genre research_article
    11 schema:inLanguage en
    12 schema:isAccessibleForFree true
    13 schema:isPartOf N0cb43ec9af024f969806f7404928a0eb
    14 N453bb6495dd74d93a503f2710ece7ee3
    15 sg:journal.1040979
    16 schema:name Bifractality of the devil’s staircase appearing in the burgers equation with brownian initial velocity
    17 schema:pagination 1151-1164
    18 schema:productId N1bc527be2efa45f3b66f595e6fb3c408
    19 Ne42645067f264518a40e58fd641dd67f
    20 Nf91a8bb6758a403882f7f01792e48e5b
    21 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042874238
    22 https://doi.org/10.1007/bf02732429
    23 schema:sdDatePublished 2019-04-10T17:30
    24 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    25 schema:sdPublisher Nb492edc384244f818f94a8a3073340aa
    26 schema:url http://link.springer.com/10.1007%2FBF02732429
    27 sgo:license sg:explorer/license/
    28 sgo:sdDataset articles
    29 rdf:type schema:ScholarlyArticle
    30 N0b270bb20e3f41d69ac9635e44d6dd35 schema:name Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304, Nice Cedex 4, France
    31 rdf:type schema:Organization
    32 N0cb43ec9af024f969806f7404928a0eb schema:volumeNumber 88
    33 rdf:type schema:PublicationVolume
    34 N1bc527be2efa45f3b66f595e6fb3c408 schema:name doi
    35 schema:value 10.1007/bf02732429
    36 rdf:type schema:PropertyValue
    37 N2f04afc8bf5a4bdbbbca12fee96b5e81 schema:name Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304, Nice Cedex 4, France
    38 rdf:type schema:Organization
    39 N453bb6495dd74d93a503f2710ece7ee3 schema:issueNumber 5-6
    40 rdf:type schema:PublicationIssue
    41 N4be59066fb884b3d8295d580cd9a4d9b rdf:first sg:person.016626051205.94
    42 rdf:rest rdf:nil
    43 N55db3ceb657f46abbb97a6a082f718d4 rdf:first sg:person.011615073661.47
    44 rdf:rest N9c0d633cde3d4c3da410cd5978adfca0
    45 N5fa95482d9b449eaad0e56330958b367 rdf:first sg:person.01104576776.49
    46 rdf:rest N55db3ceb657f46abbb97a6a082f718d4
    47 N9c0d633cde3d4c3da410cd5978adfca0 rdf:first sg:person.01262773202.94
    48 rdf:rest N4be59066fb884b3d8295d580cd9a4d9b
    49 Nb492edc384244f818f94a8a3073340aa schema:name Springer Nature - SN SciGraph project
    50 rdf:type schema:Organization
    51 Ne42645067f264518a40e58fd641dd67f schema:name dimensions_id
    52 schema:value pub.1042874238
    53 rdf:type schema:PropertyValue
    54 Nf91a8bb6758a403882f7f01792e48e5b schema:name readcube_id
    55 schema:value cc3a34aa6423a9fa50c2e2f3abfe38ad09b08ffbef501157daf665998441c8cd
    56 rdf:type schema:PropertyValue
    57 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    58 schema:name Engineering
    59 rdf:type schema:DefinedTerm
    60 anzsrc-for:0915 schema:inDefinedTermSet anzsrc-for:
    61 schema:name Interdisciplinary Engineering
    62 rdf:type schema:DefinedTerm
    63 sg:journal.1040979 schema:issn 0022-4715
    64 1572-9613
    65 schema:name Journal of Statistical Physics
    66 rdf:type schema:Periodical
    67 sg:person.01104576776.49 schema:affiliation https://www.grid.ac/institutes/grid.10548.38
    68 schema:familyName Aurell
    69 schema:givenName E.
    70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01104576776.49
    71 rdf:type schema:Person
    72 sg:person.011615073661.47 schema:affiliation N0b270bb20e3f41d69ac9635e44d6dd35
    73 schema:familyName Frisch
    74 schema:givenName U.
    75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011615073661.47
    76 rdf:type schema:Person
    77 sg:person.01262773202.94 schema:affiliation N2f04afc8bf5a4bdbbbca12fee96b5e81
    78 schema:familyName Noullez
    79 schema:givenName A.
    80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01262773202.94
    81 rdf:type schema:Person
    82 sg:person.016626051205.94 schema:affiliation https://www.grid.ac/institutes/grid.435025.5
    83 schema:familyName Blank
    84 schema:givenName M.
    85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016626051205.94
    86 rdf:type schema:Person
    87 sg:pub.10.1007/bf02096550 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001608199
    88 https://doi.org/10.1007/bf02096550
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.1007/bf02096551 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050362339
    91 https://doi.org/10.1007/bf02096551
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1103/physreva.39.268 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060478819
    94 rdf:type schema:CreativeWork
    95 https://www.grid.ac/institutes/grid.10548.38 schema:alternateName Stockholm University
    96 schema:name Center for Parallel Computers, Royal Institute of Technology, S-100 44, Stockholm, Sweden
    97 Mathematics Department, Stockholm University, S-106 91, Stockholm, Sweden
    98 rdf:type schema:Organization
    99 https://www.grid.ac/institutes/grid.435025.5 schema:alternateName Institute for Information Transmission Problems
    100 schema:name Institute for Information Transmission Problems, 101477, Moscow, Russia
    101 Observatoire de Nice, URA CNRS 1362, B.P. 4229, 06304, Nice Cedex 4, France
    102 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...