Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fano resonance scattering in waveguide with an impedance boundary
  condition   Sound propagation in a waveguide lined with one section of locally reactive
material is studied by resonance scattering approach. The objective is to
understand the effects of mode coupling in the lined section on the
transmission. It is shown that a transmission zero is present in the vicinity
of a resonance peak when a numerically real resonance frequency of the open
lined section (opened to infinities through the rigid parts of the waveguide)
is crossed. The transmission zero and immediate resonance peak form a Fano
resonance, it has been explained as an interaction between a resonance and the
non-resonant background. The real resonance frequency and its corresponding
trapped mode are formed by the interferences (couplings) between two neighbor
modes with complex resonance frequencies. It is also linked to the avoided
crossing of eigenvalues and the exceptional point. The scattering matrix is
expressed in terms of a matrix $\mathsf{H_{eff}}$ which describes approximately
the complex resonances in the open lined section. With the aid of the
eigenvalues and eigenfunctions of matrix $\mathsf{H_{eff}}$, the traditional
acoustic resonance scattering formula can be extended to describe the coupling
effects between the open lined section and the rigid parts of the waveguide.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex