Realizable response matrices of multiterminal electrical, acoustic, and elastodynamic networks at a given frequency

Abstract

We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in the three-dimensional case and in the two-dimensional case. Specifically we construct networks which realize any response matrix which is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Due to a mathematical equivalence we also obtain a characterization of the response matrices of discrete acoustic networks.

22 pages, 5 figures

References in corpus (2)

• Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors
• New metamaterials with macroscopic behavior outside that of continuum elastodynamics