HR: 0800h
AN: AE41A-0143    [Abstracts]
TI: A continuous approach to the lightning discharge
AU: * Aslan, B C
EM: aslan@math.ufl.edu
AF: Department of Mathematics, University of Florida 358 Little Hall PO Box 118105 , Gainesville, FL 32611-8105 United States
AU: Hager, W W
EM: hager@math.ufl.edu
AF: Department of Mathematics, University of Florida 358 Little Hall PO Box 118105 , Gainesville, FL 32611-8105 United States
AB: In earlier work W.W. Hager developed the following approach for modeling a lightning discharge: The continuous partial differential equation describing the electric potential was discretized, and integrated forward in time. Whenever the electric field reached the breakdown threshold in some region of the atmosphere, the associated conductivity parameter in the discrete equation was taken to infinity. An explicit formula for the limiting potential was obtained. In this poster, a continuous version of this model is introduced. First, a one-dimensional analogue of the continuous three-dimensional equation is considered, and an explicit formula for the limit of the potential as the conductivity in a subinterval of the domain tends to infinity is obtained. In the three-dimensional case, the equation is considered in spherical coordinates assuming complete symmetry. An explicit formula for the potential as the conductivity in a small neighborhood of the origin tends to infinity is obtained.
DE: 3304 Atmospheric electricity
DE: 3324 Lightning
SC: Atmospheric and Space Electricity [AE]
MN: Fall Meeting 2005