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Exact solution for the Poisson field in a semi-infinite strip.

ABSTRACT: 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.

SUBMITTER: Cohen Y

PROVIDER: S-EPMC5415694 | biostudies-literature | 2017 Apr

REPOSITORIES: biostudies-literature

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Exact solution for the Poisson field in a semi-infinite strip.

Cohen Yossi Y Rothman Daniel H DH

Proceedings. Mathematical, physical, and engineering sciences 20170419 2200

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 perturb ...[more]

PMID: 28484334

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