Coalescing particle systems and applications to nonlinear Fokker–Planck equations

Autor: Gleb Zhelezov, Ibrahim Fatkullin

Publikováno v: Zhelezov, G & Fatkullin, I 2018, ' Coalescing particle systems and applications to nonlinear Fokker–Planck equations ', Communications in Mathematical Sciences, vol. 16, no. 2, pp. 463-490 . https://doi.org/10.4310/CMS.2018.v16.n2.a8

We 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 d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::860f35e2b8ed1595ec37ff58303c8d68
https://doi.org/10.4310/cms.2018.v16.n2.a8

Limit shapes for Gibbs ensembles of partitions

Autor: Valeriy Slastikov, Ibrahim Fatkullin

Publikováno v: Fatkullin, I & Slastikov, V 2018, ' Limit Shapes for Gibbs Ensembles of Partitions ', Journal of Statistical Physics, vol. 172, no. 5, pp. 1545-1563 . https://doi.org/10.1007/s10955-018-2117-7

We explicitly compute limit shapes for several grand canonical Gibbs ensembles of partitions of integers. These ensembles appear in models of aggregation and are also related to invariant measures of zero range and coagulation-fragmentation processes

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::316b1030fa668e467c938e06434339ce
http://arxiv.org/abs/1801.00812

A study of blow-ups in the Keller–Segel model of chemotaxis

Autor: Ibrahim Fatkullin

Publikováno v: Nonlinearity. 26:81-94

We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then compared wi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc151982f0a6ca0ebac5542f21ca9be6
https://doi.org/10.1088/0951-7715/26/1/81

On spatial variations of nematic ordering

Autor: Valeriy Slastikov, Ibrahim Fatkullin

Publikováno v: Physica D: Nonlinear Phenomena. 237:2577-2586

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability den

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8c88009a89c1da24f30335df96707773
https://doi.org/10.1016/j.physd.2008.03.048

A computational strategy for multiscale systems with applications to Lorenz 96 model

Autor: Ibrahim Fatkullin, Eric Vanden-Eijnden

Publikováno v: Journal of Computational Physics. 200:605-638

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7f6741d1cf6157e53958e75fc2372f61
https://doi.org/10.1016/j.jcp.2004.04.013