Nonlinear Dynamics of the Nuclear Breeding Process View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1989

AUTHORS

V. C. Boffi , G. Spiga , P. Vestrucci

ABSTRACT

The time evolution of the nuclear breeding process, modeled as a mixture of three different species of interacting particles (neutrons, fissile and fertile atoms, respectively) diffusing in a host medium, is studied by means of the set of nonlinear integro-partial differential Boltzmann equations governing the relevant distribution functions f1, f2, f3. It is shown that the Boltzmann system for the fj’s yields, under suitable assumptions, a system of conservation equations for the number densities ρ 1, ρ 2, ρ 3, which are defined by just integrating the corresponding fj over the velocity domain. The zero-dimensional approach, for which the conservation system is a nonlinear first-order ordinary differential system, is first studied on the basis of the theory of dynamical systems, with particular regard to the stability of the fixed points. Curves representing some numerical results for the phase trajectories are presented. The space-dependent problem is then sketched, for which the conservation system can be instead of fully hyperbolic type. Finally, properties and open problems related to this latter case are shortly discussed on both mathematical and physical ground. More... »

PAGES

417-429

Book

TITLE

Noise and Nonlinear Phenomena in Nuclear Systems

ISBN

978-1-4684-5615-8
978-1-4684-5613-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4684-5613-4_32

DOI

http://dx.doi.org/10.1007/978-1-4684-5613-4_32

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001353288


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": "University of Bologna", 
          "id": "https://www.grid.ac/institutes/grid.6292.f", 
          "name": [
            "Nuclear Engineering Laboratory of the University of Bologna, Bologna, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Boffi", 
        "givenName": "V. C.", 
        "id": "sg:person.013744273135.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013744273135.71"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Bari Aldo Moro", 
          "id": "https://www.grid.ac/institutes/grid.7644.1", 
          "name": [
            "Mathematics Department of the University of Bari, Bari, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Spiga", 
        "givenName": "G.", 
        "id": "sg:person.012650736763.15", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012650736763.15"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Bologna", 
          "id": "https://www.grid.ac/institutes/grid.6292.f", 
          "name": [
            "Nuclear Engineering Laboratory of the University of Bologna, Bologna, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Vestrucci", 
        "givenName": "P.", 
        "id": "sg:person.07360753577.21", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07360753577.21"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1063/1.865372", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058118563"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1989", 
    "datePublishedReg": "1989-01-01", 
    "description": "The time evolution of the nuclear breeding process, modeled as a mixture of three different species of interacting particles (neutrons, fissile and fertile atoms, respectively) diffusing in a host medium, is studied by means of the set of nonlinear integro-partial differential Boltzmann equations governing the relevant distribution functions f1, f2, f3. It is shown that the Boltzmann system for the fj\u2019s yields, under suitable assumptions, a system of conservation equations for the number densities \u03c1 1, \u03c1 2, \u03c1 3, which are defined by just integrating the corresponding fj over the velocity domain. The zero-dimensional approach, for which the conservation system is a nonlinear first-order ordinary differential system, is first studied on the basis of the theory of dynamical systems, with particular regard to the stability of the fixed points. Curves representing some numerical results for the phase trajectories are presented. The space-dependent problem is then sketched, for which the conservation system can be instead of fully hyperbolic type. Finally, properties and open problems related to this latter case are shortly discussed on both mathematical and physical ground.", 
    "editor": [
      {
        "familyName": "Mu\u00f1oz-Cobo", 
        "givenName": "J. L.", 
        "type": "Person"
      }, 
      {
        "familyName": "Difilippo", 
        "givenName": "F. C.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4684-5613-4_32", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-1-4684-5615-8", 
        "978-1-4684-5613-4"
      ], 
      "name": "Noise and Nonlinear Phenomena in Nuclear Systems", 
      "type": "Book"
    }, 
    "name": "Nonlinear Dynamics of the Nuclear Breeding Process", 
    "pagination": "417-429", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4684-5613-4_32"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "067256c93cfd424490d225503ff15a187057807a4aafff70560c8df75e365467"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1001353288"
        ]
      }
    ], 
    "publisher": {
      "location": "Boston, MA", 
      "name": "Springer US", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4684-5613-4_32", 
      "https://app.dimensions.ai/details/publication/pub.1001353288"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T16:13", 
    "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_8675_00000243.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-1-4684-5613-4_32"
  }
]
 

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.10.1007/978-1-4684-5613-4_32'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4684-5613-4_32'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4684-5613-4_32'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4684-5613-4_32'


 

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

90 TRIPLES      23 PREDICATES      28 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4684-5613-4_32 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Ndfd1254213d2420ca4ecb4f9665e4254
4 schema:citation https://doi.org/10.1063/1.865372
5 schema:datePublished 1989
6 schema:datePublishedReg 1989-01-01
7 schema:description The time evolution of the nuclear breeding process, modeled as a mixture of three different species of interacting particles (neutrons, fissile and fertile atoms, respectively) diffusing in a host medium, is studied by means of the set of nonlinear integro-partial differential Boltzmann equations governing the relevant distribution functions f1, f2, f3. It is shown that the Boltzmann system for the fj’s yields, under suitable assumptions, a system of conservation equations for the number densities ρ 1, ρ 2, ρ 3, which are defined by just integrating the corresponding fj over the velocity domain. The zero-dimensional approach, for which the conservation system is a nonlinear first-order ordinary differential system, is first studied on the basis of the theory of dynamical systems, with particular regard to the stability of the fixed points. Curves representing some numerical results for the phase trajectories are presented. The space-dependent problem is then sketched, for which the conservation system can be instead of fully hyperbolic type. Finally, properties and open problems related to this latter case are shortly discussed on both mathematical and physical ground.
8 schema:editor Na8eea76831884a72b2189d3a4f914687
9 schema:genre chapter
10 schema:inLanguage en
11 schema:isAccessibleForFree false
12 schema:isPartOf N0781c3a187f841c2a6839c49f6d09e20
13 schema:name Nonlinear Dynamics of the Nuclear Breeding Process
14 schema:pagination 417-429
15 schema:productId N1c24fd84702945ad9dc0343a73612063
16 N4188130b17a34c38855a7707b91fab77
17 N649bfd11926f436fa65b12d8ae2500d5
18 schema:publisher N749b2548c619444481fe17f0d9db80d5
19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001353288
20 https://doi.org/10.1007/978-1-4684-5613-4_32
21 schema:sdDatePublished 2019-04-15T16:13
22 schema:sdLicense https://scigraph.springernature.com/explorer/license/
23 schema:sdPublisher N4a2f20c1af044d8987556f82e5ecbcd3
24 schema:url http://link.springer.com/10.1007/978-1-4684-5613-4_32
25 sgo:license sg:explorer/license/
26 sgo:sdDataset chapters
27 rdf:type schema:Chapter
28 N0781c3a187f841c2a6839c49f6d09e20 schema:isbn 978-1-4684-5613-4
29 978-1-4684-5615-8
30 schema:name Noise and Nonlinear Phenomena in Nuclear Systems
31 rdf:type schema:Book
32 N098106ca62394ae8b508d353fd6936ae schema:familyName Muñoz-Cobo
33 schema:givenName J. L.
34 rdf:type schema:Person
35 N1c24fd84702945ad9dc0343a73612063 schema:name doi
36 schema:value 10.1007/978-1-4684-5613-4_32
37 rdf:type schema:PropertyValue
38 N22e4ada6bf7145609f70adae7098eeef rdf:first sg:person.07360753577.21
39 rdf:rest rdf:nil
40 N25b5147b1f644bac83c9b5bebd5f9c77 rdf:first sg:person.012650736763.15
41 rdf:rest N22e4ada6bf7145609f70adae7098eeef
42 N4188130b17a34c38855a7707b91fab77 schema:name dimensions_id
43 schema:value pub.1001353288
44 rdf:type schema:PropertyValue
45 N4a2f20c1af044d8987556f82e5ecbcd3 schema:name Springer Nature - SN SciGraph project
46 rdf:type schema:Organization
47 N649bfd11926f436fa65b12d8ae2500d5 schema:name readcube_id
48 schema:value 067256c93cfd424490d225503ff15a187057807a4aafff70560c8df75e365467
49 rdf:type schema:PropertyValue
50 N674f25d1ff394fec80ebf7269ae48921 schema:familyName Difilippo
51 schema:givenName F. C.
52 rdf:type schema:Person
53 N749b2548c619444481fe17f0d9db80d5 schema:location Boston, MA
54 schema:name Springer US
55 rdf:type schema:Organisation
56 Na8eea76831884a72b2189d3a4f914687 rdf:first N098106ca62394ae8b508d353fd6936ae
57 rdf:rest Nfd9f8fa896224333be0b6dc25b47c8eb
58 Ndfd1254213d2420ca4ecb4f9665e4254 rdf:first sg:person.013744273135.71
59 rdf:rest N25b5147b1f644bac83c9b5bebd5f9c77
60 Nfd9f8fa896224333be0b6dc25b47c8eb rdf:first N674f25d1ff394fec80ebf7269ae48921
61 rdf:rest rdf:nil
62 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
63 schema:name Mathematical Sciences
64 rdf:type schema:DefinedTerm
65 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
66 schema:name Pure Mathematics
67 rdf:type schema:DefinedTerm
68 sg:person.012650736763.15 schema:affiliation https://www.grid.ac/institutes/grid.7644.1
69 schema:familyName Spiga
70 schema:givenName G.
71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012650736763.15
72 rdf:type schema:Person
73 sg:person.013744273135.71 schema:affiliation https://www.grid.ac/institutes/grid.6292.f
74 schema:familyName Boffi
75 schema:givenName V. C.
76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013744273135.71
77 rdf:type schema:Person
78 sg:person.07360753577.21 schema:affiliation https://www.grid.ac/institutes/grid.6292.f
79 schema:familyName Vestrucci
80 schema:givenName P.
81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07360753577.21
82 rdf:type schema:Person
83 https://doi.org/10.1063/1.865372 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058118563
84 rdf:type schema:CreativeWork
85 https://www.grid.ac/institutes/grid.6292.f schema:alternateName University of Bologna
86 schema:name Nuclear Engineering Laboratory of the University of Bologna, Bologna, Italy
87 rdf:type schema:Organization
88 https://www.grid.ac/institutes/grid.7644.1 schema:alternateName University of Bari Aldo Moro
89 schema:name Mathematics Department of the University of Bari, Bari, Italy
90 rdf:type schema:Organization
 




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


...