Limit shapes for Gibbs partitions of sets

Autor: Ibrahim Fatkullin, Jianfei Xue

This study extends a prior investigation of limit shapes for grand canonical Gibbs ensembles of partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes for partitions of sets, which lead

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a5da40f4d128429d0e317a4d4397149

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

Critical points of the Onsager functional on a sphere

Autor: Valeriy Slastikov, Ibrahim Fatkullin

Publikováno v: Nonlinearity. 18:2565-2580

We study Onsager's model of isotropic–nematic phase transitions with orientation parameter on a sphere. We consider two interaction potentials: the antisymmetric (with respect to orientation inversion) dipolar potential and symmetric Maier–Saupe

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::20b7ddb821fa8641ff481e4494e7f67d
https://doi.org/10.1088/0951-7715/18/6/008

[Untitled]

Autor: Ibrahim Fatkullin, Eric Vanden-Eijnden

Publikováno v: Journal of Statistical Physics. 112:155-163

The distribution of interval lengths between Brownian walkers on the line is investigated. The walkers are independent until collision; at collision, the left walker disappears, and the right walker survives with probability p. This problem arises in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f41ba6cd25d64fb76b83adf220f5fc88
https://doi.org/10.1023/a:1023627604000