A Stable Backward Monte Carlo Method for the Solution of the Boltzmann Equation View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2004

AUTHORS

Hans Kosina , Mihail Nedjalkov , Siegfried Selberherr

ABSTRACT

Backward Monte Carlo methods for solving the Boltzmann equation are investigated. A stable estimator is proposed since a previously published estimator was found to be numerically unstable. The principle of detailed balance, which is obeyed by state transitions of a physical system and ensures existence of a stable equilibrium solution, is violated by the transition probability of the unstable method, and is satisfied by construction with the proposed backward transition probability. More... »

PAGES

170-177

Book

TITLE

Large-Scale Scientific Computing

ISBN

978-3-540-21090-0
978-3-540-24588-9

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-24588-9_18

DOI

http://dx.doi.org/10.1007/978-3-540-24588-9_18

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009368075


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria", 
          "id": "http://www.grid.ac/institutes/grid.5329.d", 
          "name": [
            "Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kosina", 
        "givenName": "Hans", 
        "id": "sg:person.016550513317.72", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016550513317.72"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria", 
          "id": "http://www.grid.ac/institutes/grid.5329.d", 
          "name": [
            "Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Nedjalkov", 
        "givenName": "Mihail", 
        "id": "sg:person.011142023427.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011142023427.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria", 
          "id": "http://www.grid.ac/institutes/grid.5329.d", 
          "name": [
            "Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Selberherr", 
        "givenName": "Siegfried", 
        "id": "sg:person.013033344117.92", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013033344117.92"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2004", 
    "datePublishedReg": "2004-01-01", 
    "description": "Backward Monte Carlo methods for solving the Boltzmann equation are investigated. A stable estimator is proposed since a previously published estimator was found to be numerically unstable. The principle of detailed balance, which is obeyed by state transitions of a physical system and ensures existence of a stable equilibrium solution, is violated by the transition probability of the unstable method, and is satisfied by construction with the proposed backward transition probability.", 
    "editor": [
      {
        "familyName": "Lirkov", 
        "givenName": "Ivan", 
        "type": "Person"
      }, 
      {
        "familyName": "Margenov", 
        "givenName": "Svetozar", 
        "type": "Person"
      }, 
      {
        "familyName": "Wa\u015bniewski", 
        "givenName": "Jerzy", 
        "type": "Person"
      }, 
      {
        "familyName": "Yalamov", 
        "givenName": "Plamen", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-540-24588-9_18", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-540-21090-0", 
        "978-3-540-24588-9"
      ], 
      "name": "Large-Scale Scientific Computing", 
      "type": "Book"
    }, 
    "keywords": [
      "backward Monte Carlo method", 
      "Monte Carlo method", 
      "Boltzmann equation", 
      "Carlo method", 
      "stable equilibrium solution", 
      "transition probabilities", 
      "backward transition probability", 
      "stable estimator", 
      "physical systems", 
      "detailed balance", 
      "equilibrium solution", 
      "unstable methods", 
      "equations", 
      "estimator", 
      "state transitions", 
      "probability", 
      "solution", 
      "existence", 
      "principles", 
      "transition", 
      "system", 
      "construction", 
      "balance", 
      "method"
    ], 
    "name": "A Stable Backward Monte Carlo Method for the Solution of the Boltzmann Equation", 
    "pagination": "170-177", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1009368075"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-540-24588-9_18"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-540-24588-9_18", 
      "https://app.dimensions.ai/details/publication/pub.1009368075"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-05-20T07:44", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/chapter/chapter_26.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-540-24588-9_18"
  }
]
 

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.10.1007/978-3-540-24588-9_18'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-24588-9_18'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-24588-9_18'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-24588-9_18'


 

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

113 TRIPLES      23 PREDICATES      50 URIs      43 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-540-24588-9_18 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Nad20b366fa0646349928a531c1bcf79d
4 schema:datePublished 2004
5 schema:datePublishedReg 2004-01-01
6 schema:description Backward Monte Carlo methods for solving the Boltzmann equation are investigated. A stable estimator is proposed since a previously published estimator was found to be numerically unstable. The principle of detailed balance, which is obeyed by state transitions of a physical system and ensures existence of a stable equilibrium solution, is violated by the transition probability of the unstable method, and is satisfied by construction with the proposed backward transition probability.
7 schema:editor N85f1771bbe5a4a5eabb02de9638350da
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf Nb6ef336905784892bdae4bdb388fa3f6
12 schema:keywords Boltzmann equation
13 Carlo method
14 Monte Carlo method
15 backward Monte Carlo method
16 backward transition probability
17 balance
18 construction
19 detailed balance
20 equations
21 equilibrium solution
22 estimator
23 existence
24 method
25 physical systems
26 principles
27 probability
28 solution
29 stable equilibrium solution
30 stable estimator
31 state transitions
32 system
33 transition
34 transition probabilities
35 unstable methods
36 schema:name A Stable Backward Monte Carlo Method for the Solution of the Boltzmann Equation
37 schema:pagination 170-177
38 schema:productId Nb71fabd8860e4ac092257ba565922eb7
39 Nec0fe6202e9f4b2ca9885041804d8623
40 schema:publisher N3132e219d9814a9ea44572170d0a329c
41 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009368075
42 https://doi.org/10.1007/978-3-540-24588-9_18
43 schema:sdDatePublished 2022-05-20T07:44
44 schema:sdLicense https://scigraph.springernature.com/explorer/license/
45 schema:sdPublisher N4883e89113b449119ac04264aee4be1f
46 schema:url https://doi.org/10.1007/978-3-540-24588-9_18
47 sgo:license sg:explorer/license/
48 sgo:sdDataset chapters
49 rdf:type schema:Chapter
50 N1a0da40a455a41f3930502f2a9c78d98 rdf:first sg:person.013033344117.92
51 rdf:rest rdf:nil
52 N3132e219d9814a9ea44572170d0a329c schema:name Springer Nature
53 rdf:type schema:Organisation
54 N33dbfcee083d46d5838b8d5821ec840a schema:familyName Margenov
55 schema:givenName Svetozar
56 rdf:type schema:Person
57 N4883e89113b449119ac04264aee4be1f schema:name Springer Nature - SN SciGraph project
58 rdf:type schema:Organization
59 N5d8ed02a3f8e45f5bc504723d2f69522 schema:familyName Lirkov
60 schema:givenName Ivan
61 rdf:type schema:Person
62 N612adc3b2f79451f8b275c51907ebbab schema:familyName Yalamov
63 schema:givenName Plamen
64 rdf:type schema:Person
65 N725e3e68c3554d99baf7bab6012d2c67 schema:familyName Waśniewski
66 schema:givenName Jerzy
67 rdf:type schema:Person
68 N85f1771bbe5a4a5eabb02de9638350da rdf:first N5d8ed02a3f8e45f5bc504723d2f69522
69 rdf:rest Nd2a901d8fa04457186e687b49cce4f7f
70 N93809288c9ce4943a5160f3550899076 rdf:first sg:person.011142023427.48
71 rdf:rest N1a0da40a455a41f3930502f2a9c78d98
72 Nad20b366fa0646349928a531c1bcf79d rdf:first sg:person.016550513317.72
73 rdf:rest N93809288c9ce4943a5160f3550899076
74 Nb6ef336905784892bdae4bdb388fa3f6 schema:isbn 978-3-540-21090-0
75 978-3-540-24588-9
76 schema:name Large-Scale Scientific Computing
77 rdf:type schema:Book
78 Nb71fabd8860e4ac092257ba565922eb7 schema:name dimensions_id
79 schema:value pub.1009368075
80 rdf:type schema:PropertyValue
81 Nd2a901d8fa04457186e687b49cce4f7f rdf:first N33dbfcee083d46d5838b8d5821ec840a
82 rdf:rest Neaabdb96c1834ea8816e3f9f97e7bfac
83 Ne4b759c8fa9e4eb39c187f7cf2ee0486 rdf:first N612adc3b2f79451f8b275c51907ebbab
84 rdf:rest rdf:nil
85 Neaabdb96c1834ea8816e3f9f97e7bfac rdf:first N725e3e68c3554d99baf7bab6012d2c67
86 rdf:rest Ne4b759c8fa9e4eb39c187f7cf2ee0486
87 Nec0fe6202e9f4b2ca9885041804d8623 schema:name doi
88 schema:value 10.1007/978-3-540-24588-9_18
89 rdf:type schema:PropertyValue
90 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
91 schema:name Mathematical Sciences
92 rdf:type schema:DefinedTerm
93 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
94 schema:name Numerical and Computational Mathematics
95 rdf:type schema:DefinedTerm
96 sg:person.011142023427.48 schema:affiliation grid-institutes:grid.5329.d
97 schema:familyName Nedjalkov
98 schema:givenName Mihail
99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011142023427.48
100 rdf:type schema:Person
101 sg:person.013033344117.92 schema:affiliation grid-institutes:grid.5329.d
102 schema:familyName Selberherr
103 schema:givenName Siegfried
104 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013033344117.92
105 rdf:type schema:Person
106 sg:person.016550513317.72 schema:affiliation grid-institutes:grid.5329.d
107 schema:familyName Kosina
108 schema:givenName Hans
109 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016550513317.72
110 rdf:type schema:Person
111 grid-institutes:grid.5329.d schema:alternateName Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria
112 schema:name Institute for Microelectronics, TU-Vienna, Gusshausstrasse 27-29/E360, A-1040, Wien, Austria
113 rdf:type schema:Organization
 




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


...