{"id":"https://openalex.org/W7116100697","doi":"https://doi.org/10.48550/arxiv.2512.15058","title":"The Least Action-Augmented Lanchester Model","display_name":"The Least Action-Augmented Lanchester Model","publication_year":2025,"publication_date":"2025-12-17","ids":{"openalex":"https://openalex.org/W7116100697","doi":"https://doi.org/10.48550/arxiv.2512.15058"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.15058","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.15058","pdf_url":"https://arxiv.org/pdf/2512.15058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.15058","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Liang, Wei","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liang, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Hu, Han","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Han","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Sun, Lijie","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Lijie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Chen, Pingxing","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Pingxing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Zhong, Ming","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong, Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13371","display_name":"Military Defense Systems Analysis","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13371","display_name":"Military Defense Systems Analysis","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12888","display_name":"Military Strategy and Technology","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13494","display_name":"Military History and Strategy","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/3320","display_name":"Political Science and International Relations"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/principle-of-least-action","display_name":"principle of least action","score":0.9660000205039978},{"id":"https://openalex.org/keywords/attrition-models","display_name":"attrition models","score":0.7139999866485596},{"id":"https://openalex.org/keywords/euler-lagrange-equations","display_name":"Euler-Lagrange equations","score":0.8669999837875366},{"id":"https://openalex.org/keywords/battle-of-kursk","display_name":"Battle of Kursk","score":0.8339999914169312},{"id":"https://openalex.org/keywords/battle-of-iwo-jima","display_name":"Battle of Iwo Jima","score":0.9980000257492065},{"id":"https://openalex.org/keywords/attrition-prediction","display_name":"attrition prediction","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C2778627824","wikidata":"https://www.wikidata.org/wiki/Q178561","display_name":"Battle","level":2,"score":0.593999981880188},{"id":"https://openalex.org/C2780553607","wikidata":"https://www.wikidata.org/wiki/Q684868","display_name":"Attrition","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5253999829292297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5037999749183655},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.42590001225471497},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40130001306533813},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3601999878883362},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3366999924182892},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3361999988555908},{"id":"https://openalex.org/C2991833021","wikidata":"https://www.wikidata.org/wiki/Q361","display_name":"First world war","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2897999882698059},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.2768999934196472},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.26080000400543213}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.15058","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.15058","pdf_url":"https://arxiv.org/pdf/2512.15058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2512.15058","doi":"https://doi.org/10.48550/arxiv.2512.15058","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.15058","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.15058","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.15058","pdf_url":"https://arxiv.org/pdf/2512.15058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,79],"principle":[1,7],"of":[2,62,76,87,92,97,124],"least":[3],"action,":[4],"a":[5,22,56],"fundamental":[6],"in":[8,110,118],"variational":[9],"mechanics":[10],"with":[11,48,102],"broad":[12],"applicability":[13],"to":[14,20,46],"classical":[15,50],"physical":[16],"systems,":[17],"is":[18,82],"employed":[19],"formulate":[21],"novel":[23],"attrition":[24,121],"model":[25],"for":[26],"combat":[27,77],"dynamics.":[28],"This":[29],"formulation":[30],"extends":[31],"the":[32,42,49,90,95],"Lanchester's":[33,51,104],"square":[34,105],"law":[35],"through":[36,66,84],"second-order":[37],"temporal":[38,58],"derivatives":[39],"by":[40],"requiring":[41],"resultant":[43],"Euler-Lagrange":[44],"equation":[45],"coincide":[47],"equation.":[52],"Initial":[53],"conditions":[54,72],"at":[55],"specified":[57],"point":[59],"enable":[60],"determination":[61],"subsequent":[63],"system":[64],"evolution":[65],"action":[67],"minimization,":[68],"while":[69],"terminal":[70],"boundary":[71],"permit":[73],"backward":[74],"reconstruction":[75],"trajectories.":[78],"model's":[80],"validity":[81],"examined":[83],"historical":[85],"analysis":[86],"WWII":[88],"engagements:":[89],"Battle":[91,96],"Kursk":[93],"and":[94],"Iwo":[98],"Jima.":[99],"Comparative":[100],"studies":[101],"conventional":[103],"models":[106],"demonstrate":[107],"marked":[108],"improvements":[109],"predictive":[111],"accuracy":[112],"regarding":[113],"force":[114],"strength":[115],"progression,":[116],"particularly":[117],"capturing":[119],"non-linear":[120],"patterns":[122],"characteristic":[123],"prolonged":[125],"engagements.":[126]},"counts_by_year":[],"updated_date":"2026-09-25T08:18:29.962427","created_date":"2025-12-19T00:00:00"}