{"title":"Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions","authors":"John Toner","doi":"arxiv-2407.03071","DOIUrl":null,"url":null,"abstract":"I formulate the theory of three dimensional \"Malthusian flocks\" -- i.e.,\ncoherently moving collections of self-propelled entities (such as living\ncreatures) which are being \"born\" and \"dying\" during their motion -- whose\nconstituents all have a preference for having their velocity vectors lie\nparallel to the same two-dimensional plane. I determine the universal scaling\nexponents characterizing such systems exactly, finding that the dynamical\nexponent $z=3/2$, the \"anisotropy\" exponent $\\zeta=3/4$, and the \"roughness\"\nexponent $\\chi=-1/2$. I also give the scaling laws implied by these exponents.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"76 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.03071","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
I formulate the theory of three dimensional "Malthusian flocks" -- i.e.,
coherently moving collections of self-propelled entities (such as living
creatures) which are being "born" and "dying" during their motion -- whose
constituents all have a preference for having their velocity vectors lie
parallel to the same two-dimensional plane. I determine the universal scaling
exponents characterizing such systems exactly, finding that the dynamical
exponent $z=3/2$, the "anisotropy" exponent $\zeta=3/4$, and the "roughness"
exponent $\chi=-1/2$. I also give the scaling laws implied by these exponents.