# The change in electric potential due to lightning

William W. Hager; Beyza Caliskan Aslan

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 5, page 887-901
- ISSN: 0764-583X

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topHager, William W., and Aslan, Beyza Caliskan. "The change in electric potential due to lightning." ESAIM: Mathematical Modelling and Numerical Analysis 42.5 (2008): 887-901. <http://eudml.org/doc/250344>.

@article{Hager2008,

abstract = {
The change in the electric potential due to lightning is evaluated.
The potential along the lightning channel is a constant which is
the projection of the pre-flash potential along a piecewise harmonic
eigenfunction which is constant along the lightning channel.
The change in the potential outside the lightning channel is a harmonic
function whose boundary conditions
are expressed in terms of the pre-flash potential and
the post-flash potential along the lightning channel.
The expression for the lightning induced electric potential change is
derived both for the continuous equations, and for a spatially discretized
formulation of the continuous equations.
The results for the continuous equations are based on the properties of
the eigenvalues and eigenfunctions of the following generalized eigenproblem:
Find $u \in H_0^1 (\Omega)$, $u \ne 0$,
and $\lambda \in \mathbb\{R\}$ such that
$
\langle \nabla u, \nabla v \rangle_\{\mathcal\{L\}\} =
\lambda \langle \nabla u, \nabla v \rangle_\{\Omega\}
$
for all $v \in H_0^1 (\Omega)$, where $\Omega \subset \mathbb\{R\}^n$
is a bounded domain (a box containing the thunderstorm),
$\mathcal\{L\}$ is a subdomain (the lightning channel),
and $\langle \cdot, \cdot \rangle_\{\Omega\}$ is
the inner product
$
\langle \nabla u,\nabla v\rangle_\Omega =\int_\{\Omega\}
\nabla u\cdot\nabla v \; \{\{\rm d\}x\}.
$},

author = {Hager, William W., Aslan, Beyza Caliskan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Lightning; electric potential; Ampere's law; Maxwell's equations;
Laplacian; generalized eigenproblem; double layer potential;
complete eigenbasis.; lightning; Laplacian; complete eigenbasis},

language = {eng},

month = {7},

number = {5},

pages = {887-901},

publisher = {EDP Sciences},

title = {The change in electric potential due to lightning},

url = {http://eudml.org/doc/250344},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Hager, William W.

AU - Aslan, Beyza Caliskan

TI - The change in electric potential due to lightning

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/7//

PB - EDP Sciences

VL - 42

IS - 5

SP - 887

EP - 901

AB -
The change in the electric potential due to lightning is evaluated.
The potential along the lightning channel is a constant which is
the projection of the pre-flash potential along a piecewise harmonic
eigenfunction which is constant along the lightning channel.
The change in the potential outside the lightning channel is a harmonic
function whose boundary conditions
are expressed in terms of the pre-flash potential and
the post-flash potential along the lightning channel.
The expression for the lightning induced electric potential change is
derived both for the continuous equations, and for a spatially discretized
formulation of the continuous equations.
The results for the continuous equations are based on the properties of
the eigenvalues and eigenfunctions of the following generalized eigenproblem:
Find $u \in H_0^1 (\Omega)$, $u \ne 0$,
and $\lambda \in \mathbb{R}$ such that
$
\langle \nabla u, \nabla v \rangle_{\mathcal{L}} =
\lambda \langle \nabla u, \nabla v \rangle_{\Omega}
$
for all $v \in H_0^1 (\Omega)$, where $\Omega \subset \mathbb{R}^n$
is a bounded domain (a box containing the thunderstorm),
$\mathcal{L}$ is a subdomain (the lightning channel),
and $\langle \cdot, \cdot \rangle_{\Omega}$ is
the inner product
$
\langle \nabla u,\nabla v\rangle_\Omega =\int_{\Omega}
\nabla u\cdot\nabla v \; {{\rm d}x}.
$

LA - eng

KW - Lightning; electric potential; Ampere's law; Maxwell's equations;
Laplacian; generalized eigenproblem; double layer potential;
complete eigenbasis.; lightning; Laplacian; complete eigenbasis

UR - http://eudml.org/doc/250344

ER -

## References

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