The Dielectric Breakdown Model at Small $η$: Pole Dynamics

Details The Dielectric Breakdown Model at Small $η$: Pole Dynamics The Dielectric Breakdown Model at Small $η$: Pole Dynamics

1999-10-18

arxiv.org/abs/cond-mat/9910274v2

Physics

Condensed Matter

Soft Condensed Matter

15 pages, 4 figures; note added at end citing Sivashinsky's equation

Scientific paper

We consider the dielectric breakdown model in the limit $\eta\to 0^+$. A differential equation describing the surface growth is derived; this equation is KPZ plus a term causing linear instability, and includes a short-distance regularization similar to a viscosity. The equation exhibits an interesting dynamics in terms of poles, permitting us to derive a large family of solutions to the equation of motion. In terms of poles, we find all stationary configurations of the surface, and analytically calculate their stability. For each value of the viscosity, only one stable configuration is found, but this configuration is nonlinearly unstable in the presence of an exponentially small amount of noise. The present approach may be useful in understanding the dynamics for finite $\eta$, in particular the DLA model, in terms of perturbations to the infinitesimal $\eta$ problem.

Affiliated with

Also associated with

No associations

Rating

The Dielectric Breakdown Model at Small $η$: Pole Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Dielectric Breakdown Model at Small $η$: Pole Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Dielectric Breakdown Model at Small $η$: Pole Dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325264