Exact solution for the Poisson field in a semi-infinite strip
Author(s)Cohen, Yosef; Rothman, Daniel H
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The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.
DepartmentMassachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
Cohen, Yossi, and Daniel H. Rothman. “Exact Solution for the Poisson Field in a Semi-Infinite Strip.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 473, no. 2200 (April 2017): 20160908.
Author's final manuscript