{"id":"https://openalex.org/W7220452397","doi":"https://doi.org/10.48550/arxiv.2610.02346","title":"Traveling waves, phase separation and pattern formation in the active stepping stone model","display_name":"Traveling waves, phase separation and pattern formation in the active stepping stone model","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220452397","doi":"https://doi.org/10.48550/arxiv.2610.02346"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02346","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02346","pdf_url":"https://arxiv.org/pdf/2610.02346","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/2610.02346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120425351","display_name":"Rashmiranjan Bhutia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bhutia, Rashmiranjan","raw_affiliation_strings":["Tata Institute of Fundamental Research , Hyderabad , 500046 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research , Hyderabad , 500046 , India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077737460","display_name":"Prasad Perlekar","orcid":"https://orcid.org/0000-0002-1120-0839","observed_orcids":["https://orcid.org/0000-0002-1120-0839"]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Perlekar, Prasad","raw_affiliation_strings":["Tata Institute of Fundamental Research , Hyderabad , 500046 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research , Hyderabad , 500046 , India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051308427","display_name":"Kabir Ramola","orcid":"https://orcid.org/0000-0003-2299-6219","observed_orcids":["https://orcid.org/0000-0003-2299-6219"]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramola, Kabir","raw_affiliation_strings":["Tata Institute of Fundamental Research , Hyderabad , 500046 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research , Hyderabad , 500046 , India","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I11947397"],"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.6913999915122986,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.6913999915122986,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.18649999797344208,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11486","display_name":"Micro and Nano Robotics","score":0.04899999871850014,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/self-propulsion","display_name":"self-propulsion","score":0.8230000138282776},{"id":"https://openalex.org/keywords/birth-death-processes","display_name":"birth-death processes","score":0.6579999923706055},{"id":"https://openalex.org/keywords/invasion-waves","display_name":"invasion waves","score":0.7960000038146973},{"id":"https://openalex.org/keywords/traveling-waves","display_name":"traveling waves","score":0.9010000228881836},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"pattern formation","score":0.6899999976158142},{"id":"https://openalex.org/keywords/phase-separation","display_name":"phase separation","score":0.9430000185966492},{"id":"https://openalex.org/keywords/hydrodynamic-equations","display_name":"hydrodynamic equations","score":0.8489999771118164},{"id":"https://openalex.org/keywords/selective-advantage","display_name":"selective advantage","score":0.6660000085830688},{"id":"https://openalex.org/keywords/morphological-patterns","display_name":"morphological patterns","score":0.5360000133514404},{"id":"https://openalex.org/keywords/two-dimensional-instability","display_name":"two-dimensional instability","score":0.6159999966621399}],"concepts":[{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.7806000113487244},{"id":"https://openalex.org/C3019463535","wikidata":"https://www.wikidata.org/wiki/Q7611136","display_name":"Stepping stone","level":3,"score":0.6931999921798706},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.5949000120162964},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5004000067710876},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.49729999899864197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41290000081062317},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C77906462","wikidata":"https://www.wikidata.org/wiki/Q1140902","display_name":"Confluence","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3896999955177307},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3828999996185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3400999903678894},{"id":"https://openalex.org/C2779108282","wikidata":"https://www.wikidata.org/wiki/Q22908968","display_name":"Spatiotemporal pattern","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33149999380111694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3262999951839447},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3190000057220459},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C133256868","wikidata":"https://www.wikidata.org/wiki/Q7180940","display_name":"Phase change","level":2,"score":0.31119999289512634},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30820000171661377},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C2985264313","wikidata":"https://www.wikidata.org/wiki/Q378859","display_name":"Pattern analysis","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C2986098051","wikidata":"https://www.wikidata.org/wiki/Q1925011","display_name":"Shape change","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C95514000","wikidata":"https://www.wikidata.org/wiki/Q786897","display_name":"Autocatalytic reaction","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26750001311302185},{"id":"https://openalex.org/C2777093003","wikidata":"https://www.wikidata.org/wiki/Q6508345","display_name":"Lead (geology)","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25699999928474426},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C2780032228","wikidata":"https://www.wikidata.org/wiki/Q6865324","display_name":"Minimal model","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02346","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02346","pdf_url":"https://arxiv.org/pdf/2610.02346","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.2610.02346","doi":"https://doi.org/10.48550/arxiv.2610.02346","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02346","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02346","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02346","pdf_url":"https://arxiv.org/pdf/2610.02346","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/G3891155077","display_name":null,"funder_award_id":"RTI4007","funder_id":"https://openalex.org/F4320320715","funder_display_name":"Tata Institute of Fundamental Research"}],"funders":[{"id":"https://openalex.org/F4320320715","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220452397.pdf","grobid_xml":"https://content.openalex.org/works/W7220452397.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1674509776","https://openalex.org/W2934298210","https://openalex.org/W4394907028","https://openalex.org/W7197053386"],"related_works":["https://openalex.org/W4410243916","https://openalex.org/W7197053386","https://openalex.org/W4221147435","https://openalex.org/W2768637720","https://openalex.org/W2145689361","https://openalex.org/W3208844456","https://openalex.org/W3118347675","https://openalex.org/W3048491138","https://openalex.org/W2231757416","https://openalex.org/W2970665054"],"abstract_inverted_index":{"Selective":[0],"advantage":[1],"leads":[2,81],"to":[3,19,82,92,133,142],"the":[4,13,26,56,60,64,77,83,93,105,121,125,138],"proliferation":[5],"of":[6,22,59,79,85,107,124],"a":[7,36,40,50,116],"species":[8],"into":[9],"an":[10],"ecosystem.":[11],"On":[12],"other":[14],"hand,":[15],"self-propulsion":[16],"can":[17],"lead":[18,141],"dynamic":[20],"clustering":[21],"individuals.":[23],"To":[24],"analyze":[25,137],"intricate":[27],"effects":[28],"produced":[29],"by":[30],"such":[31,146],"competing":[32],"processes,":[33],"we":[34,62,99],"introduce":[35],"minimal":[37],"model":[38],"for":[39],"proliferating":[41],"active":[42],"population,":[43],"where":[44],"run-and-tumble":[45],"migration":[46],"is":[47],"combined":[48],"with":[49,55],"stochastic":[51],"birth-death":[52],"process.":[53,127],"Beginning":[54],"microscopic":[57],"dynamics":[58],"particles,":[61],"derive":[63],"corresponding":[65],"hydrodynamic":[66],"equations":[67],"and":[68,136],"validate":[69],"them":[70],"through":[71],"numerical":[72],"simulations.":[73],"We":[74,128],"demonstrate":[75],"that":[76,101,140],"inclusion":[78],"activity":[80,102,119],"emergence":[84],"novel":[86],"morphological":[87],"patterns,":[88],"which":[89],"are":[90],"sensitive":[91],"specific":[94],"rules":[95],"governing":[96],"migration.":[97],"Furthermore,":[98],"show":[100],"significantly":[103],"alters":[104],"characteristics":[106],"invasion":[108,126],"waves,":[109],"increasing":[110],"their":[111],"propagation":[112],"speed.":[113],"However,":[114],"beyond":[115],"threshold,":[117],"excessive":[118],"disrupts":[120],"wave-like":[122],"nature":[123],"also":[129],"extend":[130],"our":[131],"study":[132],"two":[134],"dimensions":[135],"instabilities":[139],"pattern":[143],"formation":[144],"in":[145],"systems.":[147]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}
