Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical mechanics of specular reflections from fluctuating membranes
  and interfaces   We study the density of specular reflection points in the geometrical optics
limit when light scatters off fluctuating interfaces and membranes in
thermodynamic equilibrium. We focus on the statistical mechanics of both
capillary-gravity interfaces (characterized by a surface tension) and fluid
membranes (controlled by a bending rigidity) in thermodynamic equilibrium in
two dimensions. Building on work by Berry, Nye, Longuet-Higgins and others, we
show that the statistics of specular points is fully characterized by three
fundamental length scales, namely, a correlation length $\xi$, a microscopic
length scale $\ell$ and the overall size $L$ of the interface or membrane. By
combining a scaling analysis with numerical simulations, we confirm the
existence of a scaling law for the density of specular reflection points,
$n_{spec}$, in two dimensions, given by $n_{spec}\propto\ell^{-1}$ in the limit
of thin fluctuating interfaces with the interfacial thickness $\ell\ll\xi_I$.
The density of specular reflections thus diverges for fluctuating interfaces in
the limit of vanishing thickness and shows no dependance on the interfacial
capillary-gravity correlation length $\xi_I$. Although fluid membranes under
tension also exhibit a divergence in
$n_{spec}\propto\left(\xi_M\ell\right)^{-1/2}$, the number of specular
reflections in this case can grow by decreasing the membrane correlation length
$\xi_{M}$.

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The categories of this paper are: math
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph