Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental principles for generalized Willis metamaterials   Metamaterials whose momentum is constitutively coupled with their strain show
promise in wave manipulation for engineering purposes and are called Willis
materials. They were discovered using an effective medium theory which shows
that their response is non-local in space and time. Recently, we generalized
this theory to account for piezoelectricity and demonstrated that the effective
momentum can depend constitutively on the electric field, thereby enlarging the
design space for metamaterials. Here, we develop the mathematical restrictions
on the effective properties of such generalized Willis materials, owing to
passivity, reciprocity, and causality. Establishing these restrictions is of
fundamental significance, as they test the validity of theoretical and
experimental results and applicational importance since they provide elementary
bounds for the maximal response that potential devices may achieve.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph