Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capillary Wave Scattering from a Surfactant Domain   The study of capillary wave scattering by a circular region with different
interfacial properties from the rest of an otherwise homogeneous interface is
motivated by experiments on wave attenuation at a monolayer covered air-water
interface where domains of one surface phase are dispersed in a second surface
phase. Here the scattering function is calculated for an incident wave of
frequency $\omega$ (wavevector $k_0$) scattering from an isolated circular
domain of radius $a$ with surface tension $\sigma_{1}$ which is imbedded in an
otherwise infinite interface of surface tension $\sigma_{0}$. The underlying
fluid is treated as irrotational and the three-dimensional flow problem
coupling the heterogeneous surface to the underlying liquid is reduced to a set
of dual integral equations, which are solved numerically. With this solution
the scattering amplitudes and the total scattering cross sections are
calculated as a function of the surface tension ratio $\sigma_{0}/\sigma_{1}$
and incident wavenumber $k_0 a$. The analogous problem of a discontinuous
change in bending rigidity is also considered and the solution to the complete
viscous problem is outlined in an appendix. Experimental implications of these
results are discussed.

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The categories of this paper are: gr-qc
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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: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph