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

Y. Cohen | Zendy; Daniel H. Rothman | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

Y. Cohen,

Daniel H. Rothman

Publication year - 2017

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2016.0908

Subject(s) - poisson distribution , poisson's equation , discrete poisson equation , square root , mathematical analysis , uniqueness theorem for poisson's equation , mathematics , singularity , laplace's equation , field (mathematics) , poisson's ratio , constant (computer programming) , geometry , partial differential equation , uniqueness , pure mathematics , statistics , computer science , programming language

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research