{"id":"https://openalex.org/W7223221971","doi":"https://doi.org/10.48550/arxiv.2610.30091","title":"An Implicit Conservative Finite Volume Scheme with Poisson Brackets for the Steady-State Transport of Galactic Cosmic Rays","display_name":"An Implicit Conservative Finite Volume Scheme with Poisson Brackets for the Steady-State Transport of Galactic Cosmic Rays","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223221971","doi":"https://doi.org/10.48550/arxiv.2610.30091"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30091","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30091","pdf_url":"https://arxiv.org/pdf/2610.30091","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.30091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159270357","display_name":"Weihao Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Weihao","raw_affiliation_strings":["Department of Climate and Space Sciences and Engineering , University of Michigan , Ann Arbor , MI 48109 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Climate and Space Sciences and Engineering , University of Michigan , Ann Arbor , MI 48109 , USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091814779","display_name":"Igor V. Sokolov","orcid":"https://orcid.org/0000-0002-6118-0469","observed_orcids":["https://orcid.org/0000-0002-6118-0469"]},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sokolov, Igor V.","raw_affiliation_strings":["Department of Climate and Space Sciences and Engineering , University of Michigan , Ann Arbor , MI 48109 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Climate and Space Sciences and Engineering , University of Michigan , Ann Arbor , MI 48109 , USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10251","display_name":"Solar and Space Plasma Dynamics","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10251","display_name":"Solar and Space Plasma Dynamics","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10818","display_name":"Astrophysics and Cosmic Phenomena","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.005799999926239252,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/galactic-cosmic-rays","display_name":"galactic cosmic rays","score":0.9890000224113464},{"id":"https://openalex.org/keywords/cosmic-ray-propagation","display_name":"cosmic ray propagation","score":0.8870000243186951},{"id":"https://openalex.org/keywords/implicit-finite-volume-scheme","display_name":"implicit finite volume scheme","score":0.9039999842643738},{"id":"https://openalex.org/keywords/poisson-brackets","display_name":"Poisson brackets","score":0.972000002861023},{"id":"https://openalex.org/keywords/kinetic-equations","display_name":"kinetic equations","score":0.8109999895095825},{"id":"https://openalex.org/keywords/parker-transport-equation","display_name":"Parker transport equation","score":0.7760000228881836},{"id":"https://openalex.org/keywords/total-variation-diminishing","display_name":"total variation diminishing","score":0.6639999747276306},{"id":"https://openalex.org/keywords/solar-wind","display_name":"solar wind","score":0.6460000276565552},{"id":"https://openalex.org/keywords/heliosphere","display_name":"heliosphere","score":0.8209999799728394},{"id":"https://openalex.org/keywords/ams-02","display_name":"AMS-02","score":0.843999981880188},{"id":"https://openalex.org/keywords/forbush-decreases","display_name":"Forbush decreases","score":0.878000020980835},{"id":"https://openalex.org/keywords/stream-interaction-regions","display_name":"stream interaction regions","score":0.8180000185966492}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8446999788284302},{"id":"https://openalex.org/C111309251","wikidata":"https://www.wikidata.org/wiki/Q11547","display_name":"Cosmic ray","level":2,"score":0.6996999979019165},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.47110000252723694},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.46480000019073486},{"id":"https://openalex.org/C108411613","wikidata":"https://www.wikidata.org/wiki/Q79833","display_name":"Solar wind","level":3,"score":0.44859999418258667},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.4203999936580658},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.3808000087738037},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3345000147819519},{"id":"https://openalex.org/C59496990","wikidata":"https://www.wikidata.org/wiki/Q469567","display_name":"Forbush decrease","level":5,"score":0.3343999981880188},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C29829512","wikidata":"https://www.wikidata.org/wiki/Q40218","display_name":"Spacecraft","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C54834619","wikidata":"https://www.wikidata.org/wiki/Q131687","display_name":"Heliosphere","level":4,"score":0.2906000018119812},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C32127712","wikidata":"https://www.wikidata.org/wiki/Q3366867","display_name":"Test particle","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C2777581452","wikidata":"https://www.wikidata.org/wiki/Q4363928","display_name":"Pitch angle","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30091","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30091","pdf_url":"https://arxiv.org/pdf/2610.30091","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.2610.30091","doi":"https://doi.org/10.48550/arxiv.2610.30091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30091","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.30091","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30091","pdf_url":"https://arxiv.org/pdf/2610.30091","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3364985781","display_name":"ANSWERS: Understanding and Forecasting Solar Energetic Particles in the Inner Solar System and Earth's Magnetosphere","funder_award_id":"2149771","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8491685818","display_name":null,"funder_award_id":"80NSSC23M0191","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320309292","display_name":"Princeton University","ror":"https://ror.org/00hx57361"},{"id":"https://openalex.org/F4320332374","display_name":"Ames Research Center","ror":"https://ror.org/02acart68"},{"id":"https://openalex.org/F4320332377","display_name":"Goddard Space Flight Center","ror":"https://ror.org/0171mag52"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223221971.pdf","grobid_xml":"https://content.openalex.org/works/W7223221971.grobid-xml"},"referenced_works_count":100,"referenced_works":["https://openalex.org/W337816440","https://openalex.org/W1800670681","https://openalex.org/W1940671454","https://openalex.org/W1963701191","https://openalex.org/W1964419747","https://openalex.org/W1964443169","https://openalex.org/W1972252226","https://openalex.org/W1978701658","https://openalex.org/W1980400964","https://openalex.org/W1984016121","https://openalex.org/W1989756559","https://openalex.org/W1993312058","https://openalex.org/W1997291688","https://openalex.org/W1998603859","https://openalex.org/W1998820031","https://openalex.org/W2003696978","https://openalex.org/W2005268774","https://openalex.org/W2008277413","https://openalex.org/W2013286202","https://openalex.org/W2023146293","https://openalex.org/W2023484482","https://openalex.org/W2029073306","https://openalex.org/W2038277686","https://openalex.org/W2041494519","https://openalex.org/W2045483269","https://openalex.org/W2046899724","https://openalex.org/W2049174580","https://openalex.org/W2058794574","https://openalex.org/W2064049849","https://openalex.org/W2064221922","https://openalex.org/W2069210738","https://openalex.org/W2069414247","https://openalex.org/W2075435129","https://openalex.org/W2079183135","https://openalex.org/W2081160630","https://openalex.org/W2082221208","https://openalex.org/W2087364146","https://openalex.org/W2087436998","https://openalex.org/W2090965745","https://openalex.org/W2091539461","https://openalex.org/W2120810793","https://openalex.org/W2143241075","https://openalex.org/W2153495238","https://openalex.org/W2158785365","https://openalex.org/W2167489173","https://openalex.org/W2169996752","https://openalex.org/W2170594620","https://openalex.org/W2179018237","https://openalex.org/W2190641241","https://openalex.org/W2264116441","https://openalex.org/W2481259536","https://openalex.org/W2500479599","https://openalex.org/W2512449108","https://openalex.org/W2605571548","https://openalex.org/W2757904082","https://openalex.org/W2760520718","https://openalex.org/W2766137137","https://openalex.org/W2768456981","https://openalex.org/W2791395837","https://openalex.org/W2798034958","https://openalex.org/W2809329501","https://openalex.org/W2896138793","https://openalex.org/W2944143073","https://openalex.org/W2958082132","https://openalex.org/W2980327622","https://openalex.org/W2990616747","https://openalex.org/W3007143434","https://openalex.org/W3022845766","https://openalex.org/W3062948144","https://openalex.org/W3093210518","https://openalex.org/W3107051079","https://openalex.org/W3132533630","https://openalex.org/W3212929981","https://openalex.org/W3214329827","https://openalex.org/W4200477758","https://openalex.org/W4220653922","https://openalex.org/W4220691278","https://openalex.org/W4224289328","https://openalex.org/W4281492990","https://openalex.org/W4284702237","https://openalex.org/W4315471263","https://openalex.org/W4324060374","https://openalex.org/W4379794814","https://openalex.org/W4384977802","https://openalex.org/W4387336800","https://openalex.org/W4392051748","https://openalex.org/W4392137547","https://openalex.org/W4393377595","https://openalex.org/W4394563604","https://openalex.org/W4399628480","https://openalex.org/W4401051938","https://openalex.org/W4410407167","https://openalex.org/W4413264888","https://openalex.org/W4416369065","https://openalex.org/W4416774208","https://openalex.org/W4417163888","https://openalex.org/W7133245378","https://openalex.org/W7167840700","https://openalex.org/W7203736094","https://openalex.org/W7221165891"],"related_works":["https://openalex.org/W2519294528","https://openalex.org/W4417413607","https://openalex.org/W2383401901","https://openalex.org/W2780363028","https://openalex.org/W2331212216","https://openalex.org/W2990626757","https://openalex.org/W2105942978","https://openalex.org/W4385421274","https://openalex.org/W3047006908","https://openalex.org/W3009021213"],"abstract_inverted_index":{"Galactic":[0],"cosmic":[1],"rays":[2],"(GCRs)":[3],"pose":[4],"a":[5,187],"persistent":[6],"radiation":[7],"hazard":[8],"to":[9,133,180],"astronauts":[10],"and":[11,27,35,96,192],"spacecraft":[12],"in":[13,111,142],"the":[14,24,43,59,63,89,104,116,121,134,143,165,194],"heliosphere.":[15],"Modeling":[16],"their":[17,32],"transport":[18,136],"is":[19],"essential":[20],"for":[21,42,76,99,120],"understanding":[22],"how":[23],"solar":[25,145],"wind":[26,146],"heliospheric":[28],"magnetic":[29,139],"field":[30,140],"shape":[31],"spatial":[33,94],"distributions":[34,156],"energy":[36],"spectra.":[37],"Timely":[38],"predictions":[39],"require":[40],"solving":[41],"particle":[44,86],"distribution":[45],"function":[46],"much":[47],"faster":[48,163],"than":[49,113,164],"real":[50],"time,":[51],"but":[52],"explicit":[53,105,122,166],"numerical":[54,127],"schemes":[55],"are":[56],"restricted":[57],"by":[58,126],"stability":[60],"limit":[61],"on":[62],"time":[64,100,118],"step.":[65],"In":[66],"this":[67,131],"Letter,":[68],"we":[69],"present":[70],"an":[71],"implicit":[72],"conservative":[73],"finite-volume":[74],"scheme":[75,84,132],"kinetic":[77],"equations":[78],"formulated":[79],"with":[80,177,199],"Poisson":[81],"brackets.":[82],"This":[83],"conserves":[85],"number,":[87],"maintains":[88],"total-variation-diminishing":[90],"property,":[91],"achieves":[92],"second-order":[93],"accuracy,":[95],"remains":[97],"stable":[98],"steps":[101],"far":[102],"beyond":[103],"limit,":[106],"while":[107],"reaching":[108],"quasi-steady":[109],"states":[110],"less":[112],"~1/100":[114],"of":[115],"computational":[117],"required":[119],"scheme,":[123],"as":[124],"demonstrated":[125],"tests.":[128],"We":[129],"apply":[130],"Parker":[135],"equation":[137],"along":[138],"lines":[141],"background":[144],"during":[147],"Carrington":[148],"rotation":[149],"2211,":[150],"where":[151],"it":[152],"reaches":[153],"steady-state":[154],"GCR":[155,169],"within":[157,181],"10":[158],"iterations,":[159],"about":[160],"1000":[161],"times":[162],"scheme.":[167],"The":[168,183],"proton":[170],"spectrum":[171],"averaged":[172],"over":[173],"27":[174],"days":[175],"agrees":[176],"AMS-02":[178],"measurements":[179],"10%.":[182],"simulation":[184],"also":[185],"yields":[186],"realistic":[188],"radial":[189],"intensity":[190],"gradient":[191],"captures":[193],"Forbush":[195],"decrease":[196],"features":[197],"associated":[198],"three":[200],"stream":[201],"interaction":[202],"regions":[203],"observed":[204],"at":[205],"Earth.":[206]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-23T00:00:00"}