Extended thermodynamics – consistent in order of magnitude View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2003-04

AUTHORS

I. Müller, D. Reitebuch, W. Weiss

ABSTRACT

It was always known that ordinary thermodynamics requires fairly smooth and slowly varying fields. Extended thermodynamics on the other hand is needed for rapidly changing fields with steep gradients. This notion is made explicit in the present paper by assigning orders of magnitude in steepness to the moments which are the field variables of extended thermodynamics. Once a process is deemed to be steep of O(n), the number of field variables may be read off from a table and the field equations are closed, by omission of all higher order terms. The procedure is demonstrated for stationary one-dimensional heat conduction and for heat conduction and one-dimensional motion. An instructive synthetical case of a “one-dimensional gas” is also treated and it is shown in this case how the hyperbolic equations of extended thermodynamics may be regularized – or parabolized – in a rational manner. The theory of O(n) is fully compatible with the entropy principle of that order, but no entropy postulate is needed here, at least not for closure. The theory can be shown to be compatible with an exponential phase density. More... »

PAGES

113-146

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00161-002-0106-0

DOI

http://dx.doi.org/10.1007/s00161-002-0106-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1052419035


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Technical University of Berlin", 
          "id": "https://www.grid.ac/institutes/grid.6734.6", 
          "name": [
            "Technical University Berlin, Inst. f. Verfahrenstechnik, Fasanenstr. 90, 10623 Berlin, Germany, DE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "M\u00fcller", 
        "givenName": "I.", 
        "id": "sg:person.014672007111.31", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014672007111.31"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Technical University of Berlin", 
          "id": "https://www.grid.ac/institutes/grid.6734.6", 
          "name": [
            "Technical University Berlin, Inst. f. Verfahrenstechnik, Fasanenstr. 90, 10623 Berlin, Germany, DE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Reitebuch", 
        "givenName": "D.", 
        "id": "sg:person.07642607374.19", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07642607374.19"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Technical University of Berlin", 
          "id": "https://www.grid.ac/institutes/grid.6734.6", 
          "name": [
            "Technical University Berlin, Inst. f. Verfahrenstechnik, Fasanenstr. 90, 10623 Berlin, Germany, DE"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Weiss", 
        "givenName": "W.", 
        "id": "sg:person.011735704571.46", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011735704571.46"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s001610100060", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000552635", 
          "https://doi.org/10.1007/s001610100060"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s001610100060", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000552635", 
          "https://doi.org/10.1007/s001610100060"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02179552", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003473715", 
          "https://doi.org/10.1007/bf02179552"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02179552", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003473715", 
          "https://doi.org/10.1007/bf02179552"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s001610050066", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020602659", 
          "https://doi.org/10.1007/s001610050066"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s001610050066", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020602659", 
          "https://doi.org/10.1007/s001610050066"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/b:joss.0000033155.07331.d9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048208765", 
          "https://doi.org/10.1023/b:joss.0000033155.07331.d9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160020403", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049725519"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-45892-7_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050844444", 
          "https://doi.org/10.1007/978-3-642-45892-7_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.94.511", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060462281"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.94.511", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060462281"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2003-04", 
    "datePublishedReg": "2003-04-01", 
    "description": " It was always known that ordinary thermodynamics requires fairly smooth and slowly varying fields. Extended thermodynamics on the other hand is needed for rapidly changing fields with steep gradients. This notion is made explicit in the present paper by assigning orders of magnitude in steepness to the moments which are the field variables of extended thermodynamics. Once a process is deemed to be steep of O(n), the number of field variables may be read off from a table and the field equations are closed, by omission of all higher order terms. The procedure is demonstrated for stationary one-dimensional heat conduction and for heat conduction and one-dimensional motion. An instructive synthetical case of a \u201cone-dimensional gas\u201d is also treated and it is shown in this case how the hyperbolic equations of extended thermodynamics may be regularized \u2013 or parabolized \u2013 in a rational manner. The theory of O(n) is fully compatible with the entropy principle of that order, but no entropy postulate is needed here, at least not for closure. The theory can be shown to be compatible with an exponential phase density.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00161-002-0106-0", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1135936", 
        "issn": [
          "0935-1175", 
          "1432-0959"
        ], 
        "name": "Continuum Mechanics and Thermodynamics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "15"
      }
    ], 
    "name": "Extended thermodynamics \u2013 consistent in order of magnitude", 
    "pagination": "113-146", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "f9b031cbcd9285b29cfbc4262181c48187f46fbc32321cad29c134c88b7ff103"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00161-002-0106-0"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1052419035"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00161-002-0106-0", 
      "https://app.dimensions.ai/details/publication/pub.1052419035"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T10:38", 
    "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/v90/0000000349_0000000349/records_113677_00000002.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs00161-002-0106-0"
  }
]
 

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/s00161-002-0106-0'

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/s00161-002-0106-0'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00161-002-0106-0'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00161-002-0106-0'


 

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

101 TRIPLES      21 PREDICATES      34 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00161-002-0106-0 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N6cfef0151b79414ea338aac5fefb0405
4 schema:citation sg:pub.10.1007/978-3-642-45892-7_4
5 sg:pub.10.1007/bf02179552
6 sg:pub.10.1007/s001610050066
7 sg:pub.10.1007/s001610100060
8 sg:pub.10.1023/b:joss.0000033155.07331.d9
9 https://doi.org/10.1002/cpa.3160020403
10 https://doi.org/10.1103/physrev.94.511
11 schema:datePublished 2003-04
12 schema:datePublishedReg 2003-04-01
13 schema:description It was always known that ordinary thermodynamics requires fairly smooth and slowly varying fields. Extended thermodynamics on the other hand is needed for rapidly changing fields with steep gradients. This notion is made explicit in the present paper by assigning orders of magnitude in steepness to the moments which are the field variables of extended thermodynamics. Once a process is deemed to be steep of O(n), the number of field variables may be read off from a table and the field equations are closed, by omission of all higher order terms. The procedure is demonstrated for stationary one-dimensional heat conduction and for heat conduction and one-dimensional motion. An instructive synthetical case of a “one-dimensional gas” is also treated and it is shown in this case how the hyperbolic equations of extended thermodynamics may be regularized – or parabolized – in a rational manner. The theory of O(n) is fully compatible with the entropy principle of that order, but no entropy postulate is needed here, at least not for closure. The theory can be shown to be compatible with an exponential phase density.
14 schema:genre research_article
15 schema:inLanguage en
16 schema:isAccessibleForFree false
17 schema:isPartOf N59ee91c18eb841a78960c36cc73e8281
18 Nf1c8412962564efcb0b112c03106e814
19 sg:journal.1135936
20 schema:name Extended thermodynamics – consistent in order of magnitude
21 schema:pagination 113-146
22 schema:productId N44d3be095c72432ebac11470c0954cd1
23 N5844eb2186944f9aa293e1cb1f729468
24 N8a303395f8114d108678f124991e1513
25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052419035
26 https://doi.org/10.1007/s00161-002-0106-0
27 schema:sdDatePublished 2019-04-11T10:38
28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
29 schema:sdPublisher N2f24e1e88bab44cda6351d26f89dc338
30 schema:url https://link.springer.com/10.1007%2Fs00161-002-0106-0
31 sgo:license sg:explorer/license/
32 sgo:sdDataset articles
33 rdf:type schema:ScholarlyArticle
34 N2f24e1e88bab44cda6351d26f89dc338 schema:name Springer Nature - SN SciGraph project
35 rdf:type schema:Organization
36 N44d3be095c72432ebac11470c0954cd1 schema:name doi
37 schema:value 10.1007/s00161-002-0106-0
38 rdf:type schema:PropertyValue
39 N5844eb2186944f9aa293e1cb1f729468 schema:name readcube_id
40 schema:value f9b031cbcd9285b29cfbc4262181c48187f46fbc32321cad29c134c88b7ff103
41 rdf:type schema:PropertyValue
42 N59ee91c18eb841a78960c36cc73e8281 schema:volumeNumber 15
43 rdf:type schema:PublicationVolume
44 N6cfef0151b79414ea338aac5fefb0405 rdf:first sg:person.014672007111.31
45 rdf:rest Nc93224ea91554b9ab54d410d638eb654
46 N8a303395f8114d108678f124991e1513 schema:name dimensions_id
47 schema:value pub.1052419035
48 rdf:type schema:PropertyValue
49 Na78914bc25a144d38d2e27c8fbccbcb3 rdf:first sg:person.011735704571.46
50 rdf:rest rdf:nil
51 Nc93224ea91554b9ab54d410d638eb654 rdf:first sg:person.07642607374.19
52 rdf:rest Na78914bc25a144d38d2e27c8fbccbcb3
53 Nf1c8412962564efcb0b112c03106e814 schema:issueNumber 2
54 rdf:type schema:PublicationIssue
55 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
56 schema:name Mathematical Sciences
57 rdf:type schema:DefinedTerm
58 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
59 schema:name Pure Mathematics
60 rdf:type schema:DefinedTerm
61 sg:journal.1135936 schema:issn 0935-1175
62 1432-0959
63 schema:name Continuum Mechanics and Thermodynamics
64 rdf:type schema:Periodical
65 sg:person.011735704571.46 schema:affiliation https://www.grid.ac/institutes/grid.6734.6
66 schema:familyName Weiss
67 schema:givenName W.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011735704571.46
69 rdf:type schema:Person
70 sg:person.014672007111.31 schema:affiliation https://www.grid.ac/institutes/grid.6734.6
71 schema:familyName Müller
72 schema:givenName I.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014672007111.31
74 rdf:type schema:Person
75 sg:person.07642607374.19 schema:affiliation https://www.grid.ac/institutes/grid.6734.6
76 schema:familyName Reitebuch
77 schema:givenName D.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07642607374.19
79 rdf:type schema:Person
80 sg:pub.10.1007/978-3-642-45892-7_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050844444
81 https://doi.org/10.1007/978-3-642-45892-7_4
82 rdf:type schema:CreativeWork
83 sg:pub.10.1007/bf02179552 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003473715
84 https://doi.org/10.1007/bf02179552
85 rdf:type schema:CreativeWork
86 sg:pub.10.1007/s001610050066 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020602659
87 https://doi.org/10.1007/s001610050066
88 rdf:type schema:CreativeWork
89 sg:pub.10.1007/s001610100060 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000552635
90 https://doi.org/10.1007/s001610100060
91 rdf:type schema:CreativeWork
92 sg:pub.10.1023/b:joss.0000033155.07331.d9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048208765
93 https://doi.org/10.1023/b:joss.0000033155.07331.d9
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1002/cpa.3160020403 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049725519
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1103/physrev.94.511 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060462281
98 rdf:type schema:CreativeWork
99 https://www.grid.ac/institutes/grid.6734.6 schema:alternateName Technical University of Berlin
100 schema:name Technical University Berlin, Inst. f. Verfahrenstechnik, Fasanenstr. 90, 10623 Berlin, Germany, DE
101 rdf:type schema:Organization
 




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


...