Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dielectric Breakdown Model at Small $\eta$: Pole Dynamics   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.

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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg