Ontology type: schema:ScholarlyArticle Open Access: True
2015-09
AUTHORSJosé A. Cañizo, José A. Carrillo, Francesco S. Patacchini
ABSTRACTThe existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps" it may have. The class of potentials for which we prove the existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions. More... »
PAGES1197-1217
http://scigraph.springernature.com/pub.10.1007/s00205-015-0852-3
DOIhttp://dx.doi.org/10.1007/s00205-015-0852-3
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1006835229
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/2008/1801",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Law",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/18",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Law and Legal Studies",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "University of Birmingham",
"id": "https://www.grid.ac/institutes/grid.6572.6",
"name": [
"School of Mathematics, Watson Building, University of Birmingham, Edgbaston, B152TT, Birmingham, UK"
],
"type": "Organization"
},
"familyName": "Ca\u00f1izo",
"givenName": "Jos\u00e9 A.",
"id": "sg:person.014203531443.24",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014203531443.24"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Imperial College London",
"id": "https://www.grid.ac/institutes/grid.7445.2",
"name": [
"Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK"
],
"type": "Organization"
},
"familyName": "Carrillo",
"givenName": "Jos\u00e9 A.",
"id": "sg:person.012247533740.66",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012247533740.66"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Imperial College London",
"id": "https://www.grid.ac/institutes/grid.7445.2",
"name": [
"Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK"
],
"type": "Organization"
},
"familyName": "Patacchini",
"givenName": "Francesco S.",
"id": "sg:person.010557502353.37",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010557502353.37"
],
"type": "Person"
}
],
"citation": [
{
"id": "https://doi.org/10.1016/j.anihpc.2014.09.004",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000125335"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-004-0307-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1002654113",
"https://doi.org/10.1007/s00205-004-0307-8"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.mcm.2010.03.021",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1011686253"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevlett.95.228301",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1013515757"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevlett.95.228301",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1013515757"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cphc.201000233",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019880034"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cphc.201000233",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019880034"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.aim.2012.03.036",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025322602"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.physd.2013.02.004",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1026164243"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1023/a:1023032000560",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1029874348",
"https://doi.org/10.1023/a:1023032000560"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1032264812",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-18324-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032264812",
"https://doi.org/10.1007/978-3-642-18324-9"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-18324-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032264812",
"https://doi.org/10.1007/978-3-642-18324-9"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1098/rsta.2013.0398",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032647578"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0956792514000126",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036492920"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00332-012-9132-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1037748138",
"https://doi.org/10.1007/s00332-012-9132-7"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00526-011-0427-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1038001169",
"https://doi.org/10.1007/s00526-011-0427-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00220-005-1458-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043723099",
"https://doi.org/10.1007/s00220-005-1458-7"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00220-008-0586-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043984949",
"https://doi.org/10.1007/s00220-008-0586-2"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00220-008-0586-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043984949",
"https://doi.org/10.1007/s00220-008-0586-2"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.physd.2012.10.002",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044032969"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-005-0386-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044755766",
"https://doi.org/10.1007/s00205-005-0386-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-005-0386-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044755766",
"https://doi.org/10.1007/s00205-005-0386-1"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.nonrwa.2013.12.008",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045094286"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.physd.2013.06.011",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1048506870"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1529/biophysj.105.076851",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1049625197"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-013-0644-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052823397",
"https://doi.org/10.1007/s00205-013-0644-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10955-013-0888-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1053679094",
"https://doi.org/10.1007/s10955-013-0888-4"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500028365",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054894518"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1063/1.1704928",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1057774595"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1063/1.470729",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1058049128"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0951-7715/22/3/009",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059109876"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0951-7715/24/10/002",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059110039"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/revmodphys.63.129",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060839212"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/revmodphys.63.129",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060839212"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/100804504",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062859232"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/13091779x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062870705"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1142/s0218202510004921",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062963240"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1142/s0218202511400021",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062963335"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1214/13-aap980",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064393551"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1215/00127094-2010-211",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064411279"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.3934/dcdsb.2014.19.1227",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1071736976"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.4171/rmi/376",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1072320675"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/conm/507/09960",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1089199043"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1142/4090",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1098871682"
],
"type": "CreativeWork"
}
],
"datePublished": "2015-09",
"datePublishedReg": "2015-09-01",
"description": "The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the \"gaps\" it may have. The class of potentials for which we prove the existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions.",
"genre": "research_article",
"id": "sg:pub.10.1007/s00205-015-0852-3",
"inLanguage": [
"en"
],
"isAccessibleForFree": true,
"isFundedItemOf": [
{
"id": "sg:grant.2786100",
"type": "MonetaryGrant"
}
],
"isPartOf": [
{
"id": "sg:journal.1047617",
"issn": [
"0003-9527",
"1432-0673"
],
"name": "Archive for Rational Mechanics and Analysis",
"type": "Periodical"
},
{
"issueNumber": "3",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "217"
}
],
"name": "Existence of Compactly Supported Global Minimisers for the Interaction Energy",
"pagination": "1197-1217",
"productId": [
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"208f111f4425126587363233d2464e7cc86b70b0cd068fc9016bc4cd87d10855"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s00205-015-0852-3"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1006835229"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s00205-015-0852-3",
"https://app.dimensions.ai/details/publication/pub.1006835229"
],
"sdDataset": "articles",
"sdDatePublished": "2019-04-11T09:50",
"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/v90/0000000347_0000000347/records_89786_00000000.jsonl",
"type": "ScholarlyArticle",
"url": "http://link.springer.com/10.1007%2Fs00205-015-0852-3"
}
]
Download the RDF metadata as: json-ld nt turtle xml License info
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/s00205-015-0852-3'
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/s00205-015-0852-3'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00205-015-0852-3'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00205-015-0852-3'
This table displays all metadata directly associated to this object as RDF triples.
206 TRIPLES
21 PREDICATES
66 URIs
19 LITERALS
7 BLANK NODES