A Generalization of Abrikosov's solution of the Ginzburg-Landau equations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1975-07

AUTHORS

V. G. Kogan

ABSTRACT

The Ginzburg-Landau (GL) equations for type II superconductors near the upper critical field Hc2permit a more general solution than Abrikosov's.1 It turns out that already in the first approximation it is possible to build the solution for H < Hc2.All of the basic Abrikosov results also remain correct for these expressions (Section 2). The new solutions describe the system of vortices that can form a nonperiodic structure and may contain an arbitrary number of magnetic flux quanta (Section 3). The Abrikosov structure is the particular case of the general solution (Section 3, Appendix C) in which the centers of the identical vortices form the periodic structure. The GL energy as a function of the center positions has a minimum for a periodic structure (Section 6). The validity region of these solutions is estimated. It may be wider than the similar regions for the Abrikosov case (Section 4). The simple approximate expressions for the vortex structure are obtained, and the algorithm for the higher approximations is indicated (Section 4). More... »

PAGES

103-115

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00115258

DOI

http://dx.doi.org/10.1007/bf00115258

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009666761


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel", 
          "id": "http://www.grid.ac/institutes/grid.6451.6", 
          "name": [
            "Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kogan", 
        "givenName": "V. G.", 
        "type": "Person"
      }
    ], 
    "datePublished": "1975-07", 
    "datePublishedReg": "1975-07-01", 
    "description": "The Ginzburg-Landau (GL) equations for type II superconductors near the upper critical field Hc2permit a more general solution than Abrikosov's.1 It turns out that already in the first approximation it is possible to build the solution for H < Hc2.All of the basic Abrikosov results also remain correct for these expressions (Section 2). The new solutions describe the system of vortices that can form a nonperiodic structure and may contain an arbitrary number of magnetic flux quanta (Section 3). The Abrikosov structure is the particular case of the general solution (Section 3, Appendix C) in which the centers of the identical vortices form the periodic structure. The GL energy as a function of the center positions has a minimum for a periodic structure (Section 6). The validity region of these solutions is estimated. It may be wider than the similar regions for the Abrikosov case (Section 4). The simple approximate expressions for the vortex structure are obtained, and the algorithm for the higher approximations is indicated (Section 4).", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf00115258", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1030474", 
        "issn": [
          "0022-2291", 
          "1573-7357"
        ], 
        "name": "Journal of Low Temperature Physics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "20"
      }
    ], 
    "keywords": [
      "Ginzburg-Landau equation", 
      "general solution", 
      "type-II superconductors", 
      "upper critical field", 
      "magnetic flux quanta", 
      "Abrikosov's solution", 
      "II superconductors", 
      "simple approximate expression", 
      "critical field", 
      "higher approximations", 
      "flux quantum", 
      "periodic structures", 
      "system of vortices", 
      "identical vortices", 
      "arbitrary number", 
      "approximate expression", 
      "validity region", 
      "particular case", 
      "vortex structures", 
      "first approximation", 
      "equations", 
      "approximation", 
      "nonperiodic structures", 
      "new solutions", 
      "vortices", 
      "solution", 
      "center position", 
      "Abrikosov", 
      "superconductors", 
      "generalization", 
      "quantum", 
      "algorithm", 
      "structure", 
      "field", 
      "minimum", 
      "cases", 
      "function", 
      "system", 
      "energy", 
      "number", 
      "results", 
      "region", 
      "position", 
      "similar regions", 
      "expression", 
      "center"
    ], 
    "name": "A Generalization of Abrikosov's solution of the Ginzburg-Landau equations", 
    "pagination": "103-115", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1009666761"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf00115258"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf00115258", 
      "https://app.dimensions.ai/details/publication/pub.1009666761"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-12-01T06:18", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_134.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf00115258"
  }
]
 

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/bf00115258'

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/bf00115258'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00115258'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00115258'


 

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

102 TRIPLES      20 PREDICATES      71 URIs      63 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf00115258 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nd0f31d3779c1445594818057d01df45f
4 schema:datePublished 1975-07
5 schema:datePublishedReg 1975-07-01
6 schema:description The Ginzburg-Landau (GL) equations for type II superconductors near the upper critical field Hc2permit a more general solution than Abrikosov's.1 It turns out that already in the first approximation it is possible to build the solution for H < Hc2.All of the basic Abrikosov results also remain correct for these expressions (Section 2). The new solutions describe the system of vortices that can form a nonperiodic structure and may contain an arbitrary number of magnetic flux quanta (Section 3). The Abrikosov structure is the particular case of the general solution (Section 3, Appendix C) in which the centers of the identical vortices form the periodic structure. The GL energy as a function of the center positions has a minimum for a periodic structure (Section 6). The validity region of these solutions is estimated. It may be wider than the similar regions for the Abrikosov case (Section 4). The simple approximate expressions for the vortex structure are obtained, and the algorithm for the higher approximations is indicated (Section 4).
7 schema:genre article
8 schema:isAccessibleForFree false
9 schema:isPartOf N541f50f982f5494e817911aaa68eee10
10 Nd605b20889b74ef6a0529e9810318e56
11 sg:journal.1030474
12 schema:keywords Abrikosov
13 Abrikosov's solution
14 Ginzburg-Landau equation
15 II superconductors
16 algorithm
17 approximate expression
18 approximation
19 arbitrary number
20 cases
21 center
22 center position
23 critical field
24 energy
25 equations
26 expression
27 field
28 first approximation
29 flux quantum
30 function
31 general solution
32 generalization
33 higher approximations
34 identical vortices
35 magnetic flux quanta
36 minimum
37 new solutions
38 nonperiodic structures
39 number
40 particular case
41 periodic structures
42 position
43 quantum
44 region
45 results
46 similar regions
47 simple approximate expression
48 solution
49 structure
50 superconductors
51 system
52 system of vortices
53 type-II superconductors
54 upper critical field
55 validity region
56 vortex structures
57 vortices
58 schema:name A Generalization of Abrikosov's solution of the Ginzburg-Landau equations
59 schema:pagination 103-115
60 schema:productId N74c65b215773428a9531278a3340e4f8
61 Na760ac0f2adf4308a7d955369d1e4612
62 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009666761
63 https://doi.org/10.1007/bf00115258
64 schema:sdDatePublished 2022-12-01T06:18
65 schema:sdLicense https://scigraph.springernature.com/explorer/license/
66 schema:sdPublisher N797ebb76de884a30a543e7efc3390f81
67 schema:url https://doi.org/10.1007/bf00115258
68 sgo:license sg:explorer/license/
69 sgo:sdDataset articles
70 rdf:type schema:ScholarlyArticle
71 N4d348eb00123489f8c2473816afec0e1 schema:affiliation grid-institutes:grid.6451.6
72 schema:familyName Kogan
73 schema:givenName V. G.
74 rdf:type schema:Person
75 N541f50f982f5494e817911aaa68eee10 schema:volumeNumber 20
76 rdf:type schema:PublicationVolume
77 N74c65b215773428a9531278a3340e4f8 schema:name doi
78 schema:value 10.1007/bf00115258
79 rdf:type schema:PropertyValue
80 N797ebb76de884a30a543e7efc3390f81 schema:name Springer Nature - SN SciGraph project
81 rdf:type schema:Organization
82 Na760ac0f2adf4308a7d955369d1e4612 schema:name dimensions_id
83 schema:value pub.1009666761
84 rdf:type schema:PropertyValue
85 Nd0f31d3779c1445594818057d01df45f rdf:first N4d348eb00123489f8c2473816afec0e1
86 rdf:rest rdf:nil
87 Nd605b20889b74ef6a0529e9810318e56 schema:issueNumber 1-2
88 rdf:type schema:PublicationIssue
89 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
90 schema:name Mathematical Sciences
91 rdf:type schema:DefinedTerm
92 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
93 schema:name Pure Mathematics
94 rdf:type schema:DefinedTerm
95 sg:journal.1030474 schema:issn 0022-2291
96 1573-7357
97 schema:name Journal of Low Temperature Physics
98 schema:publisher Springer Nature
99 rdf:type schema:Periodical
100 grid-institutes:grid.6451.6 schema:alternateName Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel
101 schema:name Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel
102 rdf:type schema:Organization
 




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


...