Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euler-Lagrange equations for full topology optimization of the Q-factor
  in leaky cavities   We derive Euler-Lagrange equations for the topology optimization of decay
rate in 3-d lossy optical cavities. This leads to a new class of time-harmonic
differential or integro-differential equations, which can be written as
nonlinear Maxwell systems with switching functions of special types. Our
approach is based on the notion of Pareto optimal frontier and on the
multi-parameter perturbation theory for eigenfrequencies. Parallels with
optimal control theory are discussed.

8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat