Dielectric breakdown model at small eta: pole dynamics.
We consider the dielectric breakdown model in the limit eta-->0(+). This is shown to lead to Sivashinsky's equation. We show that a particular configuration of poles is linearly stable, in analogy to the stability of the 1/2 finger for diffusion limited aggregation, and compute exactly the eigenvalues of the stability matrix.
Hastings
M B
MB
Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. hastings@cnls.lanl.gov