McDonald, N;
(2019)
Finger Growth and Selection in a Poisson Field.
Journal of Statistical Physics
10.1007/s10955-019-02454-6.
(In press).
Preview |
Text
McDonald2019_Article_FingerGrowthAndSelectionInAPoi.pdf - Published Version Download (384kB) | Preview |
Abstract
Solutions are found for the growth of infinitesimally thin, two-dimensional fingers governed by Poisson’s equation in a long strip. The analytical results determine the asymptotic paths selected by the fingers which compare well with the recent numerical results of Cohen and Rothman (J Stat Phys 167:703–712, 2017) for the case of two and three fingers. The generalisation of the method to an arbitrary number of fingers is presented and further results for four finger evolution given. The relation to the analogous problem of finger growth in a Laplacian field is also discussed.
| Type: | Article |
|---|---|
| Title: | Finger Growth and Selection in a Poisson Field |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10955-019-02454-6 |
| Publisher version: | https://doi.org/10.1007/s10955-019-02454-6 |
| Language: | English |
| Additional information: | © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Poisson paths, Laplacian growth, Free boundary problems, Conformal mapping |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10086836 |
Archive Staff Only
 |
View Item |
