Show simple item record

dc.contributor.advisorFatkullin, Ibrahimen
dc.contributor.authorZhelezov, Gleb
dc.creatorZhelezov, Gleben
dc.date.accessioned2017-06-30T15:48:28Z
dc.date.available2017-06-30T15:48:28Z
dc.date.issued2017
dc.identifier.urihttp://hdl.handle.net/10150/624562
dc.description.abstractWe study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation, such as the Patlak-Keller-Segel (PKS) model, or its multispecies variant. We then show that the presented numerical method is well-suited for the simulation of the formation of finite-time singularities in the PKS, as well as PKS pre- and post-blow-up dynamics. Additionally, we present numerical evidence that blow-up with an increasing total second moment in the two species Keller-Segel system occurs with a linearly increasing second moment in one component, and a linearly decreasing second moment in the other component.
dc.language.isoen_USen
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.subjectBessel processen
dc.subjectBlow-upen
dc.subjectCoarseningen
dc.subjectInteracting particle systemsen
dc.subjectKeller-Segelen
dc.subjectVlasov-Poissonen
dc.titleCoalescing Particle Systems and Applications to Nonlinear Fokker-Planck Equationsen_US
dc.typetexten
dc.typeElectronic Dissertationen
thesis.degree.grantorUniversity of Arizonaen
thesis.degree.leveldoctoralen
dc.contributor.committeememberFatkullin, Ibrahimen
dc.contributor.committeememberErcolani, Nicholasen
dc.contributor.committeememberSethuraman, Sunderen
dc.contributor.committeememberVenkataramani, Shankaren
dc.contributor.committeememberWehr, Janen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineMathematicsen
thesis.degree.namePh.D.en
refterms.dateFOA2018-09-11T20:58:39Z
html.description.abstractWe study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation, such as the Patlak-Keller-Segel (PKS) model, or its multispecies variant. We then show that the presented numerical method is well-suited for the simulation of the formation of finite-time singularities in the PKS, as well as PKS pre- and post-blow-up dynamics. Additionally, we present numerical evidence that blow-up with an increasing total second moment in the two species Keller-Segel system occurs with a linearly increasing second moment in one component, and a linearly decreasing second moment in the other component.


Files in this item

Thumbnail
Name:
azu_etd_15424_sip1_m.pdf
Size:
16.96Mb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record