Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical solution of many-body wave scattering problem and creating
  materials with a desired refraction coefficient   Scalar wave scattering by many small particles with impedance boundary
condition and creating material with a desired refraction coefficient are
studied. The acoustic wave scattering problem is solved asymptotically and
numerically under the assumptions $ka \ll 1, \zeta_m = \frac{h(x_m)}{a^\kappa},
d = O(a^{\frac{2-\kappa}{3}}), M = O(\frac{1}{a^{2-\kappa}}), \kappa \in
[0,1)$, where $k = 2\pi/\lambda$ is the wave number, $\lambda$ is the wave
length, $a$ is the radius of the particles, $d$ is the distance between
neighboring particles, $M$ is the total number of the particles embedded in a
bounded domain $\Omega \subset \RRR$, $\zeta_m$ is the boundary impedance of
the m\textsuperscript{th} particle $D_m$, $h \in C(D)$, $D := \bigcup_{m=1}^M
D_m$, is a given arbitrary function which satisfies Im$h \le 0$, $x_m \in
\Omega$ is the position of the m\textsuperscript{th} particle, and $1 \leq m
\leq M$. Numerical results are presented for which the number of particles
equals $10^4, 10^5$, and $10^6$.

3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an