Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spatio-temporal transfer function conditions of positive realness for
  translation invariant lattice networks of interacting linear systems   This paper is concerned with networks of interacting linear systems at sites
of a multidimensional lattice. The systems are governed by linear ODEs with
constant coefficients driven by external inputs, and their internal dynamics
and coupling with the other component systems are translation invariant. Such
systems occur, for example, in finite-difference models of large-scale flexible
structures manufactured from homogeneous materials. Using the spatio-temporal
transfer function of this translation invariant network, we establish
conditions for its positive realness in the sense of energy dissipation. The
latter is formulated in terms of block Toeplitz bilinear forms of the input and
output variables of the composite system. We also discuss quadratic stability
of the network in isolation from the environment and phonon theoretic
dispersion relations.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an